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THE 



PHYSICAL REVIEW 



A Journal op Experimental and 
Theoretical Physics 



CONDUCTED BY 

THE 

American Physical Society 



BOARD OF EDITORS 
F. BEDELL, Managing Editor 

G. K. BURGESS HENRY CREW E. L. NICHOLS 

A. D. COLE L. V. KING C. M, SPARROW 

A. C. LUNN ri. S. UHLER W. F. G. SWANN 



Vol. XVL, Series II. 



The Physical Review 

Lancaster, Pa., and Ithaca, N. Y. 

1920 



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PRESS or 

THE NEW ERA PRINTING COMPANY 
LANCASTER. PA. 



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CONTENTS OF VOL. XVI., SECOND SERIES 



JULY. 1920 



Light Absorption and Fluorescence. E. C. C. Baly i 

Note on the Adsorption of Nitrogen and Oxygen by Charcoal. Robert E. Wilson 8 

On Electromagnetic Momentum. H. A. Wilson 17 

Quantum Emission Phenomena in Radiation. David L. Webster 31 

Ionization Potentials of Argon, Nitrogen, Carbon Monoxide, Helium, Hydrogen and 

Mercury and Iodine Vapors. Clifton G. Found 41 

New Facts about Surface-Friction. Ch. Terzaghi 54 

Speeds in Signaling by the Use of Light. W. £. Forsytue 62 

Phenomena in Oxide-coated Filament Electron Tubes. H. D. Arnold 70 

Note on the End Correction in the Determination of Gas Viscosity by the Capillary Tube 

Method. Willard J. Fisher 83 

AUGUST, 1920 

The Existence of Homogeneous Groups of Large Ions. Oswald Blackwood 85 

Electrical Discharges from Pointed Conductors. John Zeleny 102 

Some Physical Properties of Nickel-Iron Alloys. L. R. Ingersoll and Others 126 

The Selective Reflection of Heat Waves by Linear Resonators. £. C. Wente 133 

The Crystal Structure of Sodium Nitrate. Ralph W. G. Wyckoff 149 

A Note on the Correction of Contact Difference of Potential Developed in Compton's 

Modification of the Quadrant Electrometer. Orro SximLMAN. Jr 158 

Note on the Electromagnetic Force between Two Atoms. G. A. Schott 162 

SEPTEMBER. 1920 

Charcoal Activation. H. Horton Sheldon 165 

The Effect of Temperature upon the Transmission of Infra-Red Radiation through 

Various Glasses. George Rosengarten i73 

The Theory of Linear-Sinoidal Oscillations. Henry G. Cordes 179 

The K-Characteristic Absorption Frequencies for the Chemical Elements Magnesium 

to Chromium. Hugo Fricke 202 

The Audion Oscillator. R. A. Heising 216 

Application of Electric Currents in the Bunsen Flame. C. W. Heaps 238 

OCTOBEJl, 1920 

The Tones from Bells. Arthur Taber Jones 247 

The Valency of Photo-electrons and the Photo-electric Properties of Some Insulators. 

M. J. Kelly 260 

The Detecting Efficiency of the Electron Tube Amplifier. E. O. Hulburt and G. 

Brbit 274 

The Minimum Arcing Voltage in Helium. K. T. Compton, E. G. Lilly. P. S. Olmstead 282 

Electrification by Impact. Harold P. Richards 290 

A New Design of Precision X-Ray Spectrometer. C. D. Cooksey 305 

The Performance of Conical Horns. G. W. Stewart 313 

The High Frequency Spectra of Lead Isotopes. C. D. Cooksey and D. Cooksey 327 

iii 



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IV CONTENTS. 

On the Variation of the Factor A in the Equation Jmr* = hv. Fernando Sanford 337 

A Study of Residual Ionization in a Gas with Reference to Temperature Effects. C. H. 

KUNSMAN 349 

American Physical Society 362 

Minutes of the One hundred and Fourth Meeting; A Catenary Loaded at one 
Point. 5. H. Anderson; Gibbs Thermodjrnamical Models, W. P. Boynton; Trans- 
parency to Total Heat Radiation, 5. L. Brown and C, E, Normand; A Study of 
the Residual Ionization in a Gas with Reference to Temperature Effects, C. H. 
Kunsman; The Continuous Spectrum of Hydrogen in the Schumann Region, R. 
P. Lewis; Multiple Reflections from the Interior of a Ring, A. A. KnowUon and 
G. A. Watt; Velocity of Sound from a Moving Source, R. B. AhhoU and J. W, 
Cook; Voltage Wave Analysis with Indicating Instruments, Leslie F. Curtis; 
The Dielectric Constant of Silk, F. J. Rogers; The Mathematical Structure of 
X-Ray Spectra, R, T. Birge; The Spectroscopic Committee of the Division of 
Physical Sciences of the National Research Council, Charles E, St. John. 

NOVEMBER, 1920 

Arcing Voltages in Mercury Vapor as a Function of the Teinperature of the Cathode. 

T. C. Hebb 375 

The Calculation of Detecting and Amplifying Properties of an Electron Tube from its 

Static Characteristics. G. Breit 387 

The Detecting Efficiency of the Single Electron Tube. E. O. Hulburt and G. Breit. 408 
Variation with Pressure of the Residual Ionization due to the Penetrating Radiation. 

K. Mel VINA Downey 420 

The Kinetic Theory of Magnetism. Warren Weaver 438 

A Photographic Method of Finding the Instantaneous Velocity of Spark Waves. Arthur 

L. Foley 449 

Is the Atom the Ultimate Magnetic Particle? Arthur H. Compton and Oswald 

Rognley 464 

On. the Free Oscillations of Spheroids. Rajendra Nath Ghosh 477 

Soft X-Rays; A Note of Interpretation. H. M. Dadourian 481 

Velocity of Sound from a Moving Source. R. B. Abbott and J. W. Cook 486 

Proceedings of the American Physical Society 493 

The Spectra of Compound Gases Flowing in Vacuum Tubes, W, H. Bair. 

DECEMBER. 1920 

On K. S. Magnet Steel. Kotaro Honda and Shozo Saito 495 

The Effect of Fluorescence and Dissociation on the Ionizing Potential of Iodine Vapor. 

H. D. Smyth and K. T. Compton 501 

The Absorption of Sound by Rigid Walls. Paul £. Sabine 514 

On the Theory of Powell's Bands and the Group- Velocity in Dispersive Media. Nihal 

Karan Seith 519 

On the X-Ray Spectra of Tungsten. William Duane and R. A. Patterson 526 

On the Effective Capacity and Resistance of a Condenser for High Frequency Currents. 

F. C. Blake 540 

The Action of Roentgen and Gamma Radiations upon the Electrical Conductivity of 

Selenium Crystals. A. M. McMahon 558 

The Effect of Temperature upon the Infra-red Absorption of Certain Glasses. G. E. 

Grantham 565 

Errata 575 

Index 576 



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Second Series July, iq20 Vol. XVI., No. i 



THE 

PHYSICAL REVIEW. 



LIGHT ABSORPTION AND FLUORESCENCE. 

By E. C. C. Baly. 

Synopsis. 

Quantitative Relationships between the Vibration Frequencies of Molecules as 
Shown by Absorption, Fluorescence^ or Phosphorescence Bands; Comparison of 
Theoretical Predictions with Experimental Results, — In an earlier paper the author 
predicted the frequencies of the absorption bands of naphthalene in the infra-red 
from the ultra-violet absorption and fluorescence. The later experimental data of 
Stang did not confirm the predicted values, and this fact caused the proposer of the 
theory to present in the present paper an explanation of the discrepancy and to give 
a generalization of the original theory. 

The lack of agreement was due to two causes: (a) the theory was dependent upon 
the alleged unsatisfactory nature of the conceptions of Bjerrum and of Kriiger, 
which relate respectively to molecular rotational velocities and to molecular preces- 
sional velocities, and (b) the experimental data upon which the hypotheses were 
based were incomplete. From a critical study of the frequencies exhibited by sulphur 
dioxide and by water vapor, the following general law of molecular frequencies is 
deduced, namely: the frequencies truly characteristic of a molecule are multiples 
of the least common multiple of the frequencies of the atoms it contains, and the 
subgroups are due to intra-molecular frequencies, that is, the least common multiples 
of groups of atoms within the molecule. 

Fluorescence of Naphthalene, — The subgroup series in the fluorescence band of 
this substance has a constant frequency difference of 1.4136 X lo**, which is now 
shown to be an intramolecular frequency instead of a true molecular frequency, as 
assumed in the earlier paper. This conclusion is justified by the chemical constitu- 
tion of the naphthalene molecule and the excellent agreement between the predicted 
frequencies and the experimental data obtained by Coblentz for ethylene. 

Fluorescence of Uranyl Salts, — In further confirmation of the hypothesis of intra- 
molecular frequencies, the author discusses (with tabulated data) the experimental 
results of Nichols and Merritt on the fluorescence bands of uranyl ammonium 
chloride and of uranyl nitrate trihydrate. 

IN a recent paper in the Physical Review/ Stang has published some 
very interesting and important measurements of the infra-red 
absorption bands exhibited by naphthalene and a few of its derivatives. 
One of the objects was to test the validity of my theory of the quantitative 

> Phys. Rev., 9, p. 542, 1917. 

I 



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2 E. C. C. BALY. [^SS! 

relationship between the various vibration frequencies possessed by 
molecules and evidenced by them as absorption, fluorescence, or phos- 
phorescence bands.^ I ventured to foretell the frequencies of the absorp- 
tion bands of naphthalene in the infra-red from the ultra-violet fluor- 
escence and absorption, and at first sight it might be a little disappointing 
to find that the values obtained by Stang do not agree with my calcula- 
tions. 

On the other hand since the date of my paper it has been found possible 
to obtain much more information as to the relationships which exist 
between the various frequencies shown by a given compound. This 
has been rendered possible by a study of the absorption spectrum of 
sulphur dioxide, for which very accurate determinations of the vibration 
frequencies in the infra-red and ultra-violet have been made. It may be 
noted here that my prediction of the infra-red spectrum of naphthalene 
was based entirely on the Bjerrum conception of molecular rotational 
frequencies and there is now little doubt that this theory together with 
the Krtiger* conception of molecular precessional velocities is not capable 
of explaining the relationships that have been observed. 

In order to find an explanation of the apparent discrepancy in the 
case of naphthalene the complete relationship found in sulphur dioxide 
may be very briefly detailed.' Every single frequency that has been 
observed with this gas can be expressed in terms of three fundamental 
frequencies, 2.4531 X 10", 8.19 X lo^S and 1.296 X 10". Of these 
2.4531 X io"ischaracteristicofoxygen,and8.i9 X 10" and 1.296 X 10" 
are characteristic of sulphur, since the infra-red bands of oxygen can be 
expressed in terms of the first, whilst those of sulphur and hydrogen 
sulphide can be expressed in terms of the last two. I have already shown 
in previous papers that the least common multiple principle forms the 
basis of molecular frequencies, and the least common multiple of the three 
fundamental frequencies given above is 2.89299 X lo*^. This number 
multiplied by 10, 12, 14, 18, 26, and 33 gives the exact central frequencies of 
all the absorption bands which have yet been observed for sulphur dioxide 
in the infra-red. Then again of these absorption bands the one with the 
central frequency 2.89299 X 14 X 10^^ has the greatest intensity, and 
this central frequency multiplied by 25 gives the exact central frequency 
of the less refrangible absorption band in the ultra-violet, the center of 
the more refrangible band not having yet been observed. 

Now it is well known that the central frequency of an absorption band 
is a true molecular frequency since it is the only frequency which persists 

* Astrophys. Journal, 42, p. 4, 191 5. 

* Ann. der Physik, 50, p. 346, 51, p. 450, 1916. 

* Baly and Garrett, Phil. Mag.. 31. p. 152, 1916. 



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Nol"i?^''] LIGHT ABSORPTION AND FLUORESCENCE. 3 

when the substance is cooled to a very low temperature. The important 
conclusion therefore is reached that the frequencies truly characteristic 
of a molecule are multiples of the least common multiple of the fre- 
quencies of the atoms it contains. 

Again the ultra-violet absorption band of sulphur dioxide consists 
of a series of subgroups symmetrically arranged round a central subgroup, 
and further each subgroup consists of a central line with a series of lines 
symmetrically arranged round it. Considering first the central lines of 
the subgroups it has been found that these form a series with constant 
frequency difference, these constant frequency differences being the 
least common multiples of two only of the atomic frequencies. Thus 
the central lines of the subgroups in the less refrangible ultra-violet 
band of sulphur dioxide form a series with constant frequency difference 
of 6.69696 X 10^^ which is the least common multiple of 8.19 X 10" and 
2.4531 X lo^^ In the more refrangible band the constant frequency 
difference between the sub-groups is 1.05972 X 10", which is the least 
common multiple of 8.19 X 10" and 1.296 X 10^. Lastly the individual 
lines within each sub-group also form a series with constant frequency 
difference, and in this case the constant frequency difference is equal 
to one of the atomic frequencies. Thus in each subgroup of the less 
refrangible ultra-violet band the component lines form a series with the 
constant frequency difference 8.19 X lo^^ 

It may be concluded from this that whilst the true molecular fre- 
quencies are multiples of the least common multiple of the frequencies 
of the atoms it contains, the subgroups are due to intra-molecular 
frequencies, that is the least common multiples of groups of atoms within 
the molecule. In case this be thought too important a deduction to 
make from one set of observations it may be stated that exactly the same 
relationship has been found in the case of the frequencies exhibited by 
water vapor. Obviously if 2.4531 X 10" is a characteristic frequency 
of oxygen it must form one of the bases of the molecular frequency system 
of water. Then we have the two intramolecular frequencies of water, 
7.5 X 10^^ and 1. 7301 X lo^^, which have been called the molecular 
rotational velocities of the water molecule. These intramolecular fre- 
quencies will be the least common multiples of two out of the three 
fundamental atomic frequencies active in the water molecule, one of 
these being 2.4531 X 10". The other two atomic frequencies are at 
once found to be 1.0635 X 10" and 2.1 159 X 10". The least common 
multiple of all three is 6.1326 X 10^ and this number multiplied by 8 
gives the exact central frequency of the great absorption band of water 
at 6.115 A<> and when multiplied by 16 the exact central frequency of the 



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4 £. C. C. BALK. [^S: 

band at 3.0575 |«. Further, by assuming an exactly analogous relation- 
ship with sulphur dioxide I have calculated the individual lines in the 
absorption band at 6.1 15 /t and these agree extraordinarily closely with 
the actual measurements made by Sleator.^ 

Apart from the somewhat obvious conflict between these relationships 
now established and the Bjerrum and Krtiger theories, they have a very 
material significance as regards the infra-red absorption of naphthalene. 
The subgroup series in the fluorescence band of naphthalene shows a 
constant frequency difference of 1.4136 X 10" (lA = 47-12). In my 
original paper I assumed on the basis of the Bjerrum theory that this 
was the molecular rotational frequency and that naphthalene should 
exhibit absorption bands in the infra-red with central frequencies of 
1.4136 X lo^* X I, 2, 3, 4, 5, etc., or wave-lengths 21.22 ^t 10.61 /jl, 
7-07 Ml 5-31 M» 4-24 M» etc. The experience now gained from sulphur 
dioxide and water shows that this frequency is not a molecular frequency 
at all, but an intra-molecular frequency due to a group of atoms within 
the naphthalene molecule, and need not necessarily appear in the infra- 
red absorption spectrum of naphthalene. 

Now if this frequency, 1. 4136 X 10^', is an intra-molecular frequency of 
naphthalene it must clearly be a true molecular frequency of a group of 
atoms in the naphthalene molecule. There are two very obvious groups 
in this molecule, namely the benzene grouping and the olefine linking. 
It is therefore to be expected that either benzene or the olefines should 
show as true molecular frequency the intra-molecular frequency of 
naphthalene, 1.4136 X 10". In other words one or the other should 
5how absorption bands with centers at 21.22/4, 10.61 m, 7.07 Mi 5-3I Mi 
4.24 Ml and further, since the intensity of the effect in naphthalene de- 
creases with the size of the multiple of 1.4136 X 10", the intensity of 
these bands should be greatest at 21.22/4 and should decrease with de- 
creasing wave-length in the series. 

It is well known that benzene does not show any of these bands but 
the infra-red absorption spectrum of ethylene has been observed by 
Coblentz between 13 fi and 3 /x.^ He finds absorption bands with centers 
at 10.5/4, 6.98/4, 5.30 /i, and 4.32/4, these being the only bands observed 
between these limits. The agreement is very striking and moreover with 
the thickness of ethylene used the amount of light absorbed was 98, 81, 
47, and 14 per cent, respectively. The sixth member of the series was 
not detected owing doubtless to its weakness and also to the presence of 
the band at 3.28 /x which does not belong to this series. Coblentz' 

» Astrophys. Journal, 48. p. 125, 1918. 

* Carnegie Inst. Publ., No. 35, 1905. Attention may be drawn to the remarkable similarity 
between the infra-red absorption spectra of the members of a homologous series. 



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Vol. XVI. 
No. I. 



1 



UGHT ABSORPTION AND FLUORESCENCE. 



5 



measurements did not extend beyond 13 m and consequently he did not 
observe the very strong band which must exist at 21.22 fi. 

It may fairly be claimed that this establishes the reality of these intra- 
molecular frequencies. Possibly also I may be excused for the error I 
made in assuming the complete validity of the Bjerrum theory which 
led me to believe that 1.4136 X 10" was a true molecular frequency of 
naphthalene. 

Reference may also be made here to the very interesting results ob- 
tained by Nichols and Merritt* upon the fluorescence spectra of uranyl 



Table I. 




l/A Diff. 




l/A Diff. 


l8t group 1469.7 20.2 - 1 X 20.2 


5th 


group 1789.1 31.4 - 2 X 15.7 


1489.9 center 




1802.8 17.7 - 1 X 17.7 


1507.1 17.2 - 1 X 17.2 




1820.5 center 


1521.8 31.9 » 2 X 15.95 




1839.4 18.9 - 1 X 18.9 


Average difference, 17.32 




1856.0 35.5 - 2 X 17.75 
Average difference, 17.25 


2d group 1538.2 35.2 « 2 X 17.6 






1553.3 20.1 - 1 X 20.1 


Central group . . 1871.2 32.8 - 2 X 16.4 


1573.4 center 




1886.1 17.9 - 1 X 17.9 


1588.9 15.5 - 1 X 15.5 




1904.0 center 


1605.1 31.7 - 2 X 15.85 




1922.6 18.6 - 1 X 18.6 


Average difference, 17.25 
3d group 1621.5 34.4 - 2 X 17.2 




1939.2 35.2 - 2 X 17.6 
Average difference, 17.42 


1638.9 17.0 - 1 X 17.0 


7th 


group 1955.3 30.9 - 2 X 15.45 


1655.9 center 




1970.1 16.1 - 1 X 16.1 


1672.8 16.9 - 1 X 16.9 




1986.2 center 


1689.4 33.5 - 2 X 16.75 




2005.7 19.5 - 1 X 19.5 


Average difference, 16.97 
4th group 1705.9 32.8 - 2 X 16.4 




2022.6 36.4 - 2 X 18.2 
Average difference, 17.45 


1719.9 18.8 - 1 X 18.8 


8th 


group 2038.3 32.7 - 2 X 16.35 


1738.7 center 




2053.3 17.7 - 1 X 17.7 


1755.4 16.7 - 1 X 16.7 




2071.0 center 


1772.2 33.5 - 2 X 16.75 




2089.0 18.0 - 1 X 18.0 
2105.9 34.9 - 2 X 17.45 


Average difference, 16.97 




2121.5 50.5 -3.x 16.83 



Average difference, 17.09 
Mean of all the subdifferences, 17.16 

salts which would seem to conform in a very remarkable way to the gen- 
eral theory of absorption and fluorescence. The diagram given by these 
authors for the fluorescence bands of uranyl ammonium chloride repre- 
sents an almost perfect example of the symmetrical distribution of the 

* Phys. Rev., 6, p. 360, 1915. 



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E. C. C, BALY. 



rSBOOMD 

LSbkbi. 



Table II. 

4th group . 



Ist group. 



1/A Dur. 

. 1629.2 14.7 - 2 X 7.35 

1637.2 6.7 - 1 X 6.7 

1643.9 center 



1667.2 23.3 - 3 X 7.77 



1677.0 33.1 - 5 X 6.62 

Average difference, 7.07 
2d group 1686.1 43.1 - 6 X 7.2 



3d group 



1699.8 


29.4 - 4 X 7.35 


1704.2 


25.0 - 3 X 8.3 


1715.2 


14.0 - 2 X 7.0 


1722.8 


6.4 - 1 X 6.4 


1729.2 


center 


1741.8 


12.6 - 2 X 6.3 


1748.6 


18.4 - 3 X 6.1 


1755.0 


25.8 - 4 X 6.45 


1765.0 


35.8 - 5 X 7.16 


Average difference. 7.02 


1772.0 


44.1 - 6 X 7.35 


1778.7 


37.4 - 5 X 7.48 


1785.9 


30.2 - 4 X 7.55 


1791.8 


24.3 - 3 X 8.1 


1802.1 


14.0 - 2 X 7.0 


1808.7 


7.4 - 1 X 7.4 


1816.1 


center 


1821.3 


5.2 - 1 X 5.2 


1828.1 


12.0 - 2 X 6.0 


1835.3 


19.2 « 3 X 6.4 


1842.4 


26.3 - 4 X 6.6 


1851.5 


35.4 - 5 X 7.1 



Average difference, 7.10 



1/A 

. 1858.7 
1865.1 
1873.0 
1877.4 
1889.0 
1895.3 
1903.0 
1908.9 
1915.9 
1923.3 
1930.1 
1938.8 



Dur. 

43.3 - 

37.9 - 

30.0 - 

25.6 - 

14.0 - 
7.7 - 

center 

5.9 - 

12.9 - 

20.3 - 

27.1 - 
35.8 « 



6 X 7.2- 
6 X7.6 
4 X7.5 
3 X8.5 
2 X7.0 
1 X7.7 

1 X.5.9 

2 X 6.45 

3 X6.8 

4 X6.8 

5 X 7.18 



Average difference, 7.24 



5th group. 



. 1945.7 
1952.9 
1959.1 
1965.3 
1976.4 
1982.3 
1989.9 
1995.9 
2002.1 
2009.8 
2017.4 
2025.0 



44.2 - 

37.0 - 

30.8 - 
24.6 B 
13.5 - 

7.6 - 
center 

6.0 - 
12.2 - 

19.9 - 
27.5 - 

35.1 « 



6 X 7.37 
5 X7.4 
4 X7.7 
3 X8.2 
2 X 6.75 
1 X7.6 

1 X6.0 

2 X6.1 

3 X6.6 

4 X6.9 

5 X7.0 



Average difference, 7.18 
6th group 2033.2 43.1 - 6 X 7.2 



2046.8 


29.5 - 4 X 7.4 


2051.0 


25.3 - 3 X 8.4 


2064.3 


12.0 - 2 X 6.0 


2070.3 


6.3 - 1 X 6.3 


2076.3 


center 


2083.8 


7.5 - 1 X 7.5 


2089.7 


13.4 - 2 X 6.7 


2103.5 


27.2 - 4 X 6.8 


2112.7 


36.4 - 5 X 7.3 



Average difference, 7.17 



Mean of the subdifferences, 7.13 

subsidiary intramolecular frequencies round the central and most strongly 
marked molecular frequency. According to my theory this .band con- 
sists of a central group with five groups on the red side and two groups 
on the blue side. Each group at ordinary temperatures consists of 
five subgroups symmetrically arranged round a central subgroup, and 
at lower temperatures these subgroups are still further resolved. This 



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J^^XVI.J LIGHT ABSORPTION AND FLUORESCENCE, J 

arrangement is very similar indeed to that already described for sulphur 
dioxide. Two constant wave number differences are present, namely 
83.20 between the centers of the groups and a secondary difference of 
1 7. 1 between the subgroups of each group. This secondary difference is 
shown in the following table and is calculated in each instance from the 
central band of the group, the average for each group being calculated 
from the total number of times the interval occurs. 
The central wave number of the band or the molecular wave number is 
1904 and this therefore should be a multiple of the wave number of an 
important band in the infra-red spectrum of uranyl ammonium chloride. 

A second fact of importance is the change in the wave number difference 
in the absorption band between the heads of the groups, this difference 
being about 71 instead of 83.2 in the fluorescence band. This is exactly 
similar to the case of sulphur dioxide as stated above, and it shows that 
the effective intramolecular or atomic frequencies are different according 
to the condition of the molecular force field of the salt. 

The grouping is still better shown in the fluorescence band of uranyl 
nitrate trihydrate which has more recently been examined.^ This band 
may be arranged in six groups, the maximum number of subgroups in 
each group being 12. The secondary differences are shown in Table II. 

In the case of the above group the principal intramolecular wave 
number is 86.8 while the secondary wave number is 7.13. It is interest- 
ing to note that the principal intramolecular wave number for the ab- 
sorption band of uranyl nitrate trihydrate is just 10 times the secondary 
wave number for the fluorescence band. 

Thb UNTVERsrry. 
Liverpool. 

» Nichols and Merritt, Phys. Rev., 9, p. 113, 191 7. 



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ROBERT E. WILSON. 



NOTE ON THE ADSORPTION OF NITROGEN AND OXYGEN 

BY CHARCOAL. 

By Robert E. Wilson. 

Synopsis. 

Discussion of Previously Published Results on the Adsorption of Oxygen, Nitrogen, 
and their Mixtures in Activated Charcoal at Liquid Air Temperatures. — This paper ia 
based on experimental data recently set forth in this Review, "Studies in the 
Adsorption of Gases by Charcoal, II.," by Lemon and Blodgett.' 

Definite Relationship between Mols of Oxygen, Nitrogen, or Mixtures Adsorbed, — 
Attention is called to the surprising £act, hitherto not mentipned. that the number of 
mols of oxygen adsorbed to any given final pressure is almost exactly 1.30 times the 
number of mols of nitrogen adsorbed to the same final pressure. The pressure vs, 
volume adsorbed curve for pure oxygen and for mixtures of oxygen and nitrogen 
can, therefore, be very accurately calculated from the results obtained with nitrogen 
alone. Furthermore, it is also possible to reproduce all the curves representing the 
rate of adsorption from the results obtained with nitrogen alone. 

Bearing of Foregoing Relationship on Theory of Adsorption; Nature of Forces by 
which Gas Molecules are Held. — By a mathematical treatment of the foregoing data, 
it can be demonstrated that neither Langmuir's one layer adsorption theory (which 
undoubtedly applies to that portion of the gas held with the greatest tenacity) nor the 
"capillary condensation theory " (which applies to loosely held liquid in capillaries 
of moderate size) are applicable to the intermediate range of pressures covered by 
Lemon and Blodgett's data. Their results can, however, be explained on the basis 
of the following hypotheses: (i) the ratio of the molecular volume of adsorbed nitro- 
gen to that of adsorbed oxygen is the same as for the free liquids (1.31 at — 192* C.) ; 
(2) the gases are held in layers several molecules deep primarily by the attractive 
force of the charcoal surface; (3) the stray field around oxygen and nitrogen mole- 
cules is substantially the same at any given distance. 

SOME very interesting data have recently been published in this 
journal by Lemon and others, on the adsorption of various gases 
by charcoal. In the second of that series of articles Lemon and Blodgett* 
describe the results of a series of experiments on the adsorption of oxygen 
and nitrogen and mixtures of the two by charcoal. In these experiments 
various amounts of oxygen or nitrogen or their mixtures were suddenly 
admitted to a chamber containing an activated and previously evacuated 
specimen of cocoanut-shell charcoal at liquid air temperature. The 
rate of decrease in pressure and the final equilibrium pressure attained 
by each mixture was recorded and presented in tabular or graphic form 
in the article. On the basis of the results therein detailed it was con- 
» Physical Revibw, XIV., s, November, 1919. 



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No^i^^^l ADSORPTION OP NITROGEN AND OXYGEN. g 

eluded that oxygen and nitrogen are not adsorbed independently, but 
no attempt was made to point out any definite relationship between the 
adsorption of the two gases and their mixtures. 

A close study of the data therein presented brings to light, however, an 
extremely interesting fact which seems to have considerable bearing on 
the question of the mechanism of adsorption. Although at first sight 
there appears to be no simple relationship between the results obtained 
on the adsorption of oxygen and of nitrogen, as a matter of fact if 
the simple assumption is made that one mol of nitrogen is in every way 
equivalent to 1.30 mols of oxygen, it is possible to calculate not only the 
results obtained with pure oxygen, but also those for various mixtures 
of the two gases, by using merely the data obtained with pure nitrogen. 

Since the observed points on the three curves do not exactly correspond, 



Fig. 1. 

Agreement between calculated and observed values of final pressures of oxygen and mixtures 
of oxygen and nitrogen absorbed in charcoal. 

the best way to test the above assumption is to calculate from one nitrogen 
observation to a point which should lie on the smooth curve connecting 
the observed points for oxygen or the mixtures. These smooth curves 



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10 



ROBERT £. WILSON. 



fSBCOND 

LSbkxss. 



are obtained by plotting the log of the final pressure against the parts of 
gas adsorbed (see Fig. i corresponding to Fig. 5 of the original article). 

The method of making these calculations is as follows: If one mol of 
nitrogen is exactly equivalent to 1.30 mols of oxygen, then 130 parts Oi 
should give the same log final p as that given by 100 parts Ni (0.270). 
Similarly the observed pressures for 80 parts N2 should exactly correspond 
to 1.3 X 80 = 104 parts O2. By calculating the five observed nitrogen 
points over to their oxygen equivalent in this manner, the five crosses 
on the oxygen curve were obtained. As will be observed, these agree 
remarkably closely with the smooth curve drawn through the circles 
which represent the observed points on the oxygen curve. In a similar 
manner, it is possible to calculate points on the mixture curve, using 
only the observed points for nitrogen; and it will be observed that again 
the agreement between the calculated points and the observed curve is 
excellent. 

Another way to show the agreement between the calculated and 
observed values is to calculate values corresponding to each observed 
point for oxygen or the mixtures from the corresponding points on the 
smooth curve connecting the nitrogen observations. The agreement 
thus obtained is shown in Table I. 

Table I. 



Putter. 


PUttA's. 


Should - ParU A^s. 


Log > Calculated. 


Log >Ob- 
•erred. 


DUrerence. 


125 





96.2 


9.86 


9.85 


-0.01 


100 





76.8 


7.88 


7.90 


-fO.02 


90 





69.2 


7.38 


7.43 


-fO.05 


75 





57.7 


6.84 


6.89 


+0.05 


50 





38.5 


6.30 


6.26 


-0.04 


75 


25 


82.7 


8.39 


8.38 


-0.01 


50 


50 


88.5 


8.98 


8.97 


-0.01 


35 


65 


91.9 


9.36 


9.33 


-0.03 


20 


80 


95.4 


9.74 


9.S9 


-0.05 


10 


90 


97.7 


9.98 


9.95 


-0.03 



Small deviations, of course, occur in plotting a smooth curve through 
any series of points, so that the *' calculated" values themselves cannot 
be considered especially precise even if the theory were exact. 

It is thus possible from a single series of observations on different 
amounts of nitrogen to calculate very accurately the corresponding 
curves for oxygen, and for mixtures of oxygen and nitrogen, merely by 
assuming that one mol of nitrogen is exactly equivalent to 1.30 mols of 



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nSJTi!^^*] adsorption of nitrogen and oxygen. I I 

oxygen. Furthermore, even the curves for the rate of adsorption may 
be reproduced very closely by making the same assumption. For ex- 
ample, the rate curve for 80 parts N2 should, by the above method of 
calculation, lie between the curve for 100 parts O2 (= 76.8 parts Ni) 
and that for 75 parts O2 and 25 parts Nj (= 82.7 parts N2); and as a 
matter of fact this is found to be the case when the three curves (taken 
from Figs. 2 and 4 of original article) are plotted on the same co5rdinates 



i 

^ 



Fig. 2. 
Correspondence between rates of adsorption of pure gases and mixtures. 

as in Fig. 2 of this article. By similar interpolation it is possible to 
approximate any other rate curve for the results for nitrogen alone. 

This remarkable parallelism between the adsorption of oxygen and 
nitrogen, extending as it does over a variation in final pressures of nearly 
ten thousand-fold, should certainly throw some light on the mechanism 
of the adsorption of these two gases. As in any case where adsorption 
takes place inside capillaries of unknown size and number, there is a 
wide variety of assumptions which can be made to explain any set of 
known facts providing a sufficient number of variables are introduced. 
It is the purpose of this note, however, to call attention to an extremely 



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12 ROBERT E. WILSON. ^SSS 

simple assumption which seems to explain adequately all the foregoing 
facts. 

An important question which should be considered at the outset is 
whether the gases are adsorbed in films one layer deep, as Langmuir has 
demonstrated to be the case in certain examples of adsorption, or whether 
they are several layers deep, possibly completely filling the smaller 
capillaries. In this particular case both the amount of gas adsorbed and 
the pressure which it exerts definitely support the latter view. Hulett 
and others have shown that well-activated charcoal holds very consider- 
able amounts of oxygen and nitrogen even in a good vacuiun at high 
temperatures. This firmly held gas would certainly seem to be that 
which is adsorbed in a layer one molecule deep. Since its pressure is 
inappreciable even at temperatures of 200--300® C, it would certainly 
not be measurable at liquid air temperatures. Furthermore, as the tem- 
perature is lowered and approaches the condensing point of the gases, 
the amounts of gas adsorbed increase greatly — certainly to more than 
ten-fold those held at the higher temperatures. It would appear, there- 
fore, that only a small fraction of the gas adsorbed in the experiments 
described by Lemon and Blodgett could be held in the layer one molecule 
deep, and that the measurably high vapor pressures recorded were pro- 
duced by the last portions of the gas which were held but loosely in 
layers possibly 8 or 10 molecules distant from the charcoal surface. 

As a first step, then, it seems reasonable to assume that the above 
mentioned definite ratio between the number of mols of the different 
gases adsorbed to any given final pressure, might correspond to the rela- 
tive molecular volumes occupied by the adsorbed gases, which at liquid 
air temperatures would presumably approximate the liquid state. The 
best data on the densities of liquid oxygen and nitrogen seem to be those 
of Baly and Donnan^ who give the following figures for the density of 
liquid oxygen as a function of the absolute temperature in the vicinity 
of its boiling point. (The figures are rounded.) 

d02 = 1.249 - o.oo48(r - 68), 

dN2 = 0.854 - 0.0048(r - 68). 

Assuming liquid air temperature to be — 192® C, this gives the densi- 
ties as 1. 1 87 and 0.792 respectively, which corresponds to relative 
molecular volumes of 1.310 for N2 to i for O2. It will be observed that 
this is remarkably close to the ratio of 1.30 determined from the adsorp- 
tion measurements. Certainly the agreement seems too close to be 
considered a coincidence, in view of the relationship which might reason- 
ably be expected to exist between these two quantities. 

» J. Chem. Soc.. 81. 911. 



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Vol. XVI; 
No. r 



1 



ADSORPTION OF NITROGEN AND OXYGEN. 



13 



These simple and apparenriy reasonable results do not, however, fit 
in well with the customary explanation of the absorption of gases in 
capillaries — the "capillary condensation" theory. This theory assumes 
that adsorption in a porous material such as charcoal is almost entirely 
(except for the first layer of molecules) due to the known fact that the 
vapor pressure of a liquid inside a fine capillary, the walls of which are 
wet by the liquid, decreases greatly with the decrease in the diameter of 
the capillary. This law may be expressed quantitatively as follows:* 

,„P ^L. 

P RTpr 

or in more convenient form for calculations: 

P 2.085X7 



HHiAr* 


Valttetftt -i92®C. 




ForOi. 


ForNt. 


P « vapor pressure of free liquid 


25.2 cm} 

15.73« 

26.95 

81.1 


114 cm.i 


^ = " " of absorbed liquid 




X ■= surface tension in dynes/cm 


8.27« 


V » molal volume of liquid 


35.30 


T ■= absolute temp, in ®C 


81.1 


d ■= diameter of capillaries 





Using these figures, if the vapor pressure lowering in the case under 
consideration is due to capillary condensation the pressure of condensed 
oxygen should be: 

10.90 



\ogpOi = 1. 401 — 



io*d 



and for nitrogen 



log /)N, = 2.056-^, 



where d is the diameter of the largest capillaries in which the condensed 
liquid is held (since this part of the liquid is responsible for the observed 
final pressures). 

From the foregoing it should be possible to calculate the diameter of 
the capillaries which would correspond to different final pressures of 
oxygen or nitrogen, and then find, by referring to Fig. i, the number of 

» For derivation see R. v. Helmholtz, Wied. Ann.. 27, 508, 1886. 

* Baly, Phil. Mag., 49, 517. 1900. 

• Values for — 193® C. by Baly and Donnan, Trans. Chem. Soc., 81, 907, 1902, 



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H 



ROBERT E. WILSON. 



rSacoHB 
LSkuks. 



parts of oxygen or nitrogen which were actually adsorbed between these 
pressure limits. Table II. summarizes the results of such calculations. 

Table II. 



Diameter of 

CapUlariet 

Centimeten. 


C«lc. log > of Oi, 


Calc.lof>of A^t. 


Putt of 0» 
Condeneed. 


Pwttof lit 


Ratio. 


a-2xio->... 

2-3X10-V.. 
3-4XlO->... 


-00 to -4.05 
-4.05 to -2.23 
-2.23 to -1.33 


-00 to -1.69 
-1.69 to - .44 
- .44 to -f .18 


35 
62 
15 


82 

12 

5 


0.23 

5.2 

3.0 



In other words, a given set of capillaries (o — 2 X lo"* cm.) appear to 
take up more than four times as much oxygen as nitrogen, but the next 
largest group of capillaries (2 — 3 X lO"*) condense over five times 
as much nitrogen as oxygen! Furthermore, practically all of the gas 
adsorbed would appear to be held in capillaries whose diameters lie 
between the narrow limits of i and 5 X 10"* cm. Since these absurd 
results follow necessarily from the mathematical application of the capil- 
lary condensation theory, it must be concluded that the theory is not 
applicable for such small capillaries, although its validity seems to be 
established for the larger capillaries where the lowering of vapor pressure 
is only very slight. 

Since neither the one-layer adsorption theory nor the capillary con- 
densation theory appears to apply to the intermediate range of pressures 
covered by Lemon and Blodgett's work, it seems desirable to develop 
some new conceptions to explain the surprising results pointed out pre- 
viously in this paper. If, for example, it be assumed that the primary 
reason for the low vapor pressure is the attraction of the charcoal surface 
for the gases, the vapor pressure of the adsorbed oxygen and nitrogen 
would then depend only upon their distance from the charcoal surfaces 
and upon their own stray fields of force. If the stray fields of force of 
the two kinds of molecules are equal at a given distance, and the relative 
volumes of the condensed gases are as J ^> 1.30^ as seems probable from 
the density data, then it would follow as a necessary conclusion that a 
given sample of charcoal at any definite temperature and any final 
pressure would hold 1.30 times as many mols of oxygen as of nitrogen. 
Since this is in precise accord with the observed facts, and the assumptions 
are not only simple but justified by other known facts, this would seem 
to be a very satisfactory working hypothesis in the light of the information 
at present available. 

It may at first sight seem unlikely that oxygen and nitrogen should 
have equal stray fields at any given distance from their center, in view 



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Vol. XVI.T 
No. I. J 



ADSORPTION OP NITROGEN AND OXYGEN. 



15 



of the fa.ct that their boiling points differ by about 12® C. This di- 
vergence could, however, be entirely accounted for by the fact that the 
molecules of oxygen come closer together in the liquid state and hence 
the attractive forces of these molecules for one another would be some- 
what greater, even though the stray field at any given distance were 
exactly the same as that for nitrogen. 

It must, of course, be admitted that certain other more complicated 
assumptions might be made to explain the same facts; for example, the 
capillary condensation theory, or indeed almost any theory, could be 
explained by assuming that the ratio of the molal volumes of the ad- 
sorbed gases varied widely from the 1.30 which seems most reasonable, 
coupled with certain very arbitrary assiunptions as to the gradation in 
the sizes of the pores in the particular sample of charcoal used. The 
writer has followed several of these more complicated hypotheses through 
to their logical conclusion without finding one of enough value to justify 
its detailed presentation as a possible substitute for the foregoing theory, 
at least in the light of the data at present available. 

In conclusion, although Langmuir's theory of one layer adsorption 



^yk/^iwy ^ Wtf<imw<w» ^ ^H ^ m wr j -r 




Fig. 3. 

appears to be well established for the small amounts of gas which are 
held with extreme tenacity on a solid surface, and although the capillary 
condensation theory seems to adequately explain the slightly depressed 
vapor pressures in capillaries of moderate size, there is a wide intermediate 
range of adsorption covered by Lemon and Blodgett's work in which 



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1 6 ROBERT E, WILSON. 

neither theory seems to be satisfactory. The range over which different 
types of adsorption appear to hold are shown roughly in Fig. 3, which 
represents a typical adsorption curve for charcoal over the whole range 
of volumes and pressures.^ 

To explain the results obtained in this intermediate region, the following 
hypotheses are therefore suggested : • 

1. The ratio between the molecular volumes of adsorbed oxygen and 
nitrogen is very close to the ratio between the molecular volumes of the 
free liquids at the same temperature (about i to 1.30). 

2. The stray field around oxygen molecules is substantially the same 
as that around nitrogen molecules at any given distance. 

3. The gases are held primarily by the attractive force of the charcoal 
surface, in layers more than one molecule deep, and not by capillary 
condensation. 

These hypotheses adequately explain the known facts, and require no 
assumptions whatever as to the gradation in the sizes of the pores in the 
charcoal, or as to the functional relationship between the distance from 
the charcoal surface and its attractive force. 

It would be extremely interesting to compare the similar results ob- 
tained by varying the gases, the charcoal, or the temperature from that 
prevailing in these experiments. Data obtained along these lines should 
serve either to definitely verify or discredit the foregoing hypotheses. 

Rbsbarch Laboratory of Applied Chemistry, 
Massachusetts Institute of Technology. 

1 See article by the writer and others in J. Ind. Eng. Chem.. 11, 420, 1919. 



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X?J"i?^^] ELECTROMAGNETIC MOMENTUM. 1 7 



ON ELECTROMAGNETIC MOMENTUM. 
By H. a. Wilson. 

Synopsis. 

PuMdamenUU nUUions involving eUctromagnetic momentum. — ^A simple way of 
deducing the force per unit volume acting in the electromagnetic field is given 
which makes clear the nature of the force in terms of elementary ideas. The well- 
known relation between the Jlux of energy and the momentum in the field suggests 
that all momentum is due to energy flux. Starting with this assumption a simple 
relation is obtained between the momentum, energy and velocity of the center of mass 
of any sjrstem. This relation when applied to a single particle leads to the same 
relations between the longitudinal and transverse masses and the velocity as have 
been deduced from the principle of relativity. Several particular examples are 
discussed. 

Relations of matter and ether to stresses. — It is argued that since the electro- 
magnetic field has momentum, energy and is subject to gravitational attraction it 
therefore poss ess e s all the essential properties of matter and that therefore the 
stresses in the field should be regarded as acting through the field and on it in the 
same way that stresses act in ordinary matter. When there is a resultant force 
on a space containing matter the force is supposed to act on the matter and not 
on the ether in the space and the motion of matter and the stresses in it are not 
supposed to act on the ether or to tend to set it in motion. We should therefore 
regard the stresses in the electromagnetic field as acting on the field and not on 
the ether. There is therefore no more reason to suppose that the ether is set in 
motion in an electromagnetic field than there is for supposing that it is set in motion 
by the stresses in or the motion of ordinary matter. 

The transmission of energy and momentum in the field. — This is considered from 
the point of view indicated. The theory is similar to that given by E. Cunningham 
who however regards the motion in the field as motion of the ether. Cunningham 
also supposes that the velocity is always equal to the velocity of light. I have 
not adopted this assumption but instead I suppose that the direction of the velocity 
of the field coincides with the direction of the momentum in the field. In this 
way the fiux of energy in the field is explained as partly due to the working of the 
stresses in the field and partly to convection of energy with the moving field. Several 
examples are discussed. Finally some results are mentioned which follow from 
the idea that energy is subject to gravitational attraction, 

THE hypothesis that momentum can exist in an electromagnetic 
field or in the ether was first put forward by J. J. Thomson in 
1893 and was afterwards developed by Poincar6 and Abraham. It now 
forms part of the generally accepted electromagnetic theory. 

If F denotes the total force on the electricity inside a closed surface 5 
then it may be shown that 

F ^ \ (Maxwell's Stresses) ^^ -\ \ J^ [d>h]da, 



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1 8 H. A. WILSON. [IJSS 

where a denotes the volume enclosed by 5; c is the velocity of light; 
d denotes the electric and h the magnetic intensity. Thus it appears 
that the resultant of the stresses acting across the surface S is greater 
than the total force acting on the electricity inside S by an amount 



-cli^"-'^'" 



This integral has therefore been said to represent a mechanical force 
acting on the ether inside 5 which it is natural to suppose is made up of* 
forces (d/dt)[d'h]/c per unit volume. The nature of this mechanical 
force may be made clear in the following way. 

According to Maxwell's theory a displacement current (d) produces 
the sariie magnetic field as an equal conduction current. The force on a 
current in a magnetic field is undoubtedly duetto the interaction of the 
magnetic field of the current with the external field so that we should 
expect *a force on a displacement current equal to that on a conduction 
current. We should therefore expect a force equal to [d'h]/c per unit 
volume on the displacement current d when in a magnetic field of strength 
h since the force on a conduction current of density i is [i'h]/c per unit 
volume. 

A varying magnetic field may be said to produce a magnetic dis- 
placement current h which produces an electric field opposite in direction 
but otherwise precisely analogous to the magnetic field due to a current. 
We should therefore expect a force on a magnetic displacement current 
when in an electric field of amount [d-h]/c per unit volume. 

The total force per unit volume is therefore 

[d-h]/c + [d-h]/c = -^j^[d-h] 

which agrees with the usual result. Since force is equal to momentum 
communicated per unit time the existence of this force (i/c){d/dt)[d-h] 
has therefore led to the view that there is in the electromagnetic field or 
in the ether an amount of mechanical momentum equal to [d'h]/c per 
unit volume. 

J. J. Thomson supposes this momentum to be the momentum of 
moving tubes of electric force which on his theory give rise to the mag- 
netic field. 

It appears that in the electromagnetic field there is momentum [d-h]/c 
associated with a flux of energy c[d'h], A similar result^ has been 
deduced from the principle of relativity namely that the convection of 
energy by a moving body implies an amount of momentum equal to 
the product of the energy and velocity divided by c^. 

» Relativity and the Electron Theory, E. Cunningham, p. 80. 



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Nc^i^^'] ELECTROMAGNETIC MOMENTUM. 1 9 

It seems probable therefore that a flux of energy is always associated 
with an amount of momentum equal to the flux divided by c*. It is 
natural therefore to regard this momentum as due to inertia of the 
energy and to regard all momentum as due to a flux of energy. Consider 
any material system moving in any manner with reference to co5rdinates 
X, y, z. Let E denote the energy density at any point in the system 
and let the flux of energy per unit area per unit time be denoted by F, 
Then if 2 denotes the x co6rdinate of the center of mass of the energy 
in the system we have 

^ " fEdS ' 

where dS denotes an element of voluftie. Differentiating this with 
respect to the time / and lyriting S for J^EdS this gives 

Si = fxEdS. 

Now £ = — div F, so that 

Si ^ - fx div FdS, 

If the integration is extended over a volume so large that F is zero over 
the surface enclosing it this gives 

Si = fFJLS, 

where F, denotes the x component of F. If now we suppose that a 
flux of -energy F, in the x direction is associated with x momentum per 
unit volume equal to F^jc^ we get 

JI/x=^/F^5, 

where JIf, denotes the total momentum of the system, due to energy 
flux, in the x direction. Hence 

Si = M^\ 

Thus it appears that the total momentum of the system due to energy 
flux is equal to the total energy in the system multiplied by the velocity 
of the center of mass of the energy in the system and divided by (?. 
If all momentum is due to energy flux then the center of mass of the 
energy will coincide with the center of mass of the system. 

^ fin example consider a condenser consisting of two large parallel 
plates kept at a fixed distance 5 apart by means of insulating blocks. 
Let the electric intensity between the plates be d and let the condenser 
be moving with a velocity v in a direction perpendicular to the planes 
of its plates. 



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20 H. A. WILSON, . ^5SS! 

The energy density between the plates is (P/2 and the flux of energy 
between the plates is zero since there is no magnetic field. The plates 
attract each other with a force d^/2 per unit area so that there will be a 
pressure in the blocks separating the plates equal to A(P/2, where A is 
the area of each plate. There is therefore a flux of energy in the blocks 
equal to A(Pv/2 so that if we take » to be along the x direction 

fFJLS = -^~ . 

The momentum due to the flux of energy is therefore 

AdHsl2c^t 

which is equal to the electricah energy Asd^/2 multiplied by »/c*. 

Charging the condenser therefore increases^ its momentum in a direc- 
tion perpendicular to its planes although there is no flow of electromag- 
netic energy in this case. We may observe that between the plates 
there is a tension d*/2 and a density of energy d*/2 which produces a 
flow due to convection wP/2 so that the total energy flux is zero what- 
ever the value of v in agreement with the value of c[d'h] in this case. 

Now consider the case when the condenser moves in a direction 
parallel to the planes of its plates. When v is very small compared with 
c we get a magnetic field between the plates equal to vd/c and perpendic- 
ular to V and d. There is therefore a flow of energy between the plates 
equal to c[d'h] = wP which gives for the electromagnetic momentum 
Asvd^/c*. There is also a tension in the plates in the direction of v 
equal to ^sd^{i — t^/c^) which gives a flow of energy per unit length in 
the plates equal to ivsd^{i — ^/c^) in the opposite direction to v. The 
momentum corresponding to this is — iAsvd^{i — t^/c^)/(? so that the 
total momentum is 

The electromagnetic energy is equal to 

As Asvd^ ( ^\ 

so that 

Sv Asvd^. . .,„ 
^ = -^^ (I + t^/^). 

which agrees with the value just found for the momentum as was to be 
expected. 

As another example consider the Lorentz electron, which when at 
rest is a thin hollow sphere of electricity of radius a and charge e, WTien 



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No!"if^^'l ELECTROMAGNETIC MOMENTUM. 21 

moving with velocity v in the x direction it contracts into a spheroid of 
revolution with axes 

a Vi — v*/c*, a and a. ' 

The electromagnetic momentum of the Lorentz electron calculated by 
integrating [d'h]lc is equal to 

where fi = vjc. The sum of the electric and magnetic energies is equal to 

TG 24(1 - /?)* • 

Thus the electromagnetic momentum is not equal to the electromagnetic 
energy multiplied by »/c*. 

In order to maintain the electricity in equilibrium it is necessary, as 
was shown by Poincar6, to suppose that it is pulled inwards by an in- 
ternal stress the x component of which must be equal to ^/32ir*a*. The 
work done by this stress when v is increased from zero to c is equal to the 
stress multiplied by the volume ^va^ of the sphere so that we may 
suppose that there is energy inside the sphere of amount ^/32ir*a* per 
unit volume. 

The flux of energy inside the sphere is therefore zero since there is a 
tension in the direction of motion equal to the energy density. The 
internal energy therefore does not contribute anything to the momen- 
tum. The total energy is therefore 

^ 3 + /P _f_ 4 ,, _ M\\ ^ 

Ta 24(1 - /?)* "^ 2>2i^a^ 3 ""^ ^^ ^^ " 6Ta(i - /?)* • 

Multiplying this by v/c* = file we get 

which is equal to the momentum. It appears that when the energy 
inside the sphere is taken into account the momentum of the Lorentz 
electron is equal to its total energy multiplied by vjc^ as it should be. 

If a force F acts on a particle moving in the direction of the force then 
FH = bM and FvH = «S so that vbM =55 which with M = 5v/c* 
gives 5 = 5o(i — v^/c^)^^ where So is the energy of the particle when 
r = o. This result is a well-known deduction from the principle of 
relativity. The momentum of the particle due to energy flux is therefore 
given by 



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2 2 H. A, WILSON. [^SSS! 

The transverse mass m' of the particle due to energy flux is given by 
tn' = Mlv = SoC-^(i - v'lc^Ti 

s 

and the longitudinal mass m" due to energy flux by 
m" = dMIdv = 5oC-^(i - i;*/c*)-*. 

The ratio of the transverse mass m' to the longitudinal mass m" is there- 
fore 

These results will be true for a particle of any kind. They will there- 
fore be true for any of the different types of electrons which have been 
proposed. It follows that the measurements of e/m for electrons for 
different values of v, made by Kaufmann, Bucherer and others do not 
really enable us to decide in favor of any particular type. The results 
obtained agree with the view that momentum is due to energy flux but 
if this view is correct than the variation of m with v is the same for any 
sort of particle whether composed of electricity or not. 

If all momentum is due to energy flux then we should expect all energy 
to be subject to gravitational attraction. This is confirmed by the 
recent discovery of the deflection of light by the gravitational field of 
the sun. 

The force represented by {i/c)(d/di)[d'h] has usually been regarded as a 
force acting on the ether. Thus H. A. Lorentz says that in consequence 
of the existence of this force we must either regard the ether as having 
so great a density that its motion due to this force is negligible or else 
we must regard Maxwell's stresses as imaginary ones, merely auxiliary 
mathematical quantities not representing real stresses.^ 

In ordinary mechanics we deal with stresses acting in material bodies 
which are supposed to move through the ether withovt setting it in 
motion. For example when power is transmitted from one pulley to 
another by means of a belt we have a flux of energy along the belt which 
is partly a convection of kinetic energy equal to ^pv^ X v where p is 
the density and v the velocity of the material of the belt and partly a 
transmission of energy due to work done by the tension T in the belt 
equal to — Tv per unit area of cross-section of the belt. 

Now the ultimate particles of the matter composing the belt are 
believed to be some sort of ethereal modifications which move through 
the unmodified ether without setting it in motion presumably by a 
process of growing in front and fading away behind. Thus in ordinary 

* Theory of Electrons, p. 31. 



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No!*!^^'*! ELECTROMAGNETIC MOMENTUM. 23 

mechahics forces act on ethereal modifications and energy is transmitted 
by stresses existing in such modifications when they move through the 
ether. When there is a resultant force on a portion of sp>ace we do not 
regard this force as tending to set the ether in the space in motion but 
only as tending to produce a motion of the ethereal modification or 
matter there present. 

The electroms^^netic field is like matter in that it is believed to be 
some sort of modification of the ether. Like matter it can move through 
the ether and possesses energy and momentum and is object to gravita- 
tional attraction. It seems therefore that we ought to regard the force 
{i/c){d/dt)[d'h] as acting not on the ether but on the ethereal modification 
present that is on the electromagnetic field. If we adopt this view then 
we may regard the ether as always at rest and the Maxwell's stresses as 
acting through the field so that when these stresses give a resultant force 
on a portion of space then this force tends to produce a motion of the 
ethereal modifications present in the portion of space whether the modi- 
fications present consist of matter, electricity or only an electroms^^netic 
field. This way of regarding the matter is consistent with our con- 
ceptions of the nature of matter and the transmission of energy through 
ordinary matter in motion. Force, as we know it, is something which 
tends to change the motion through the ether of an ethereal modification 
without setting the ether itself in motion. The motion of the ethereal 
modification is really a process of change of state and not motion at 
all but for convenience may be referred to as a motion through the ether. 
A force does work on the moving matter although there is really only 
change of state and no motion. This involves no contradiction because 
in the definition of work nothing is said about the nature of the process 
by which the matter acted on by the force moves. 

If the observed effects of force are really only changes of state in a 
stagnant ether then there is no reason to suppose that the ether can ever 
be set in motion. We may still speak of matter as moving through the 
ether provided we understand that the expression merely refers to the 
change of position and not to the nature of the process by which the 
change takes place. 

If we regard the force {i/c)(d/dt)[d'h] as acting on the electromagnetic 
field then we must regard the momentum [d'h]/c as due to a motion in 
the field. We have seen that this momentum can be regarded as due 
to the flux of energy so that it is natural to conclude that the flux of 
energy is the motion in the field to which the momentum is due. 

Now the flux of energy may be made up of two parts, a convection 
of the energy present per unit volume through the ether with a velocity v 



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24 H. A. WILSON, gSJS 

that IS |(d* + A')» and a flux due to work done by stress. The velocity v 
may be taken to be in the direction of the momentum and the energy 
flux that is along the direction of the vector [d-h]. The velocity v is 
the velocity with which the field moves through the ether. The process 
by which this motion takes place being the same as the process by which 
matter moves through the ether. Presumably a process of growing in 
front and fading away behind by changes of state in a stagnant ether. 
In the case of light waves moving with velocity c such a process is merely 
wave motion in tHe usual sense. It may be objected that we ought not 
on this view to regard any energy as moving by a process of convection 
but it must be understood that the process of convection is of the same 
nature as the convection of energy by a moving particle which also 
moves by a process of change of state. Thus what we call convection is 
really very much of the same nature as wave motion but it is convenient 
to express what happens in the electromagnetic field in terms of ideas 
derived from experience with matter in bulk. The statement that some 
of the energy in the field moves by a process of convection is intended to 
be understood as meaning convection like that by a moving particle 
which moves by changes of state in a stagnant ether. 

In the same way the flux of momentum may be due partly to con- 
vection of momentum and partly to stress in the field. The Maxwell 
stresses of course represent the total flow of momentum. 

At a point in an electromagnetic field suppose the momentum [d'h]/c 
is directed along the x axis and let d be along the y axis and let the angle 
between d and A be ^ so that hy =^ h cos 6 and h, = h sin 6. 

Consider a small plane area a and let the direction cosines of its 
normal be /, m, n. Let Xnt Yr! , Zn be the components of the stresses 
acting across a. Then if q be written for [d-h]lc the flux of energy along 
the normal to a is Iqc^ so that we have 

- Xn'v + Elv = lqc\ (i) 

where v denotes the velocity of the field which is alpng x and E denotes 
the energy density ^{d^ + V). 
The flux of X momentum across a will be given by 

Xn' - qlv = Xn. (2) 

where Xn denotes the x component of the Maxwell's stress across a. 

The fluxes of y and z momentum will be given by Yn = Yn and Zn 
= Zn simply because all the momentum in the field is x momentum so 
that there is no convection of 3^ or 2 momentum. 

Now when d is along y and A, = o as we are supposing to be the case 



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Nol^if^'l ELECTROMAGNETIC MOMENTUM, 25 

we have 

Jfn = - hKd^ + A^) = - IE. 

Substituting this value of Xn in (2) we get 

XJ = qlv - IE. 
Hence (i) becomes 

which gives 



2Ev — gt* = qc^, 
E /ff ■ 



q \ ^ 

One root is less than c and the other greater. Presumably the one less 
than c should be taken. 

A calculation similar in principle to the above has been published 
previously by E. Cunningham who however regards the velocity v as 
that of the ether, whereas I prefer to regard it as the velocity of the 
electromagnetic field through the ether. 

In the case of light waves we have E = iP- and q = (P/c so that » = c. 
This means that in light waves the field moves along through the ether 
with the velocity c as was to be expected. Cunningham however con- 
cludes that in light waves the ether moves along with the light with the 
velocity c of light so that the waves are at rest relative to the ether. 

Cunningham also does not assume that the velocity is along the 
direction of [d'h] but he assumes that the resultant velocity of the ether 
is always equal to c. It seems to me to be much more reasonable to 
assume that the velocity is along the direction of [d'h]. For all the 
momentum is in this direction and we should naturally expect the velocity 
of the field to be in the same direction as the momentum. 

We have 

Xn' = qlv + Xn 

= Kqv - £) 

= -HE? -'q'c\ 

so that there is a pressure in the x direction. In the case of light waves 
travelling along x if we take d along y as before then h will be along z so 
that e =» 90*", £ = d*, (? = d?lc and A = d. Hence 

Xn' =-/V£2-g2^2 =^0, 
Yn' = Fn = O. 
Zn' = Zn = O. 

Thus in light there is no stress, as was shown by Cunningham, but simply 
the field moving through the ether carrying its energy and momentum 
with it. 



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26 H. A, WILSON. [^S? 

This result at first sight appears to be inconsistent with the wave 
theory of light but the paradox is only apparent. The motion of the 
field through the ether must be supposed to take place by a process of 
growing in front and fading away behind of some form of modification 
of the ether. The modification being the presence of electric and mag- 
netic fields. This is clearly the same thing as is usually meant by the 
wave theory. The calculation given above shows that the flux of energy 
in the electromagnetic field can be explained on mechanical principles 
as due to convection and the working of stresses in the moving field. 
By mechanical principles we mean the ordinary mechanical processes 
which are supposed to take place in moving matter. The electromagnetic 
theory is more fundamental than our ideas of mechcmical processes so 
that when electromagnetic theory is interpreted mechanically we have to 
use the ideas of convection and motion through the ether derived from 
experience with matter in bulk instead of the more fundamental idea 
of wave motion or motion by a process of change of state in a sts^ant 
medium. 

The equation 



-zt 



in the case when d and h are at right angles reduces to either v = ch/d 
or r = cd/h. The proper value to take is presumably the one which is 
less than c. 

When d and h are at right angles and h less than d the relation between 
V, h and d is the same as in the theory of J. J. Thomson, in which h is 
supposed to be due to the motion of the electric tubes of force. We may 
remark that J. J. Thomson's theory is especially successful when applied 
to cases in which d and h are at right angles and h less than d. 

It appears that the flow of energy in an electromagnetic field can be 
explained on mechanical principles. The energy is transmitted partly 
by convection due to motion of the field through the ether and partly 
by the working of stresses in the moving field. The ether remains at 
rest and in fact does not enter into consideration at all. The momentum 
in the field is regarded as associated with the energy flux and the velocity 
of the field is along the direction of the momentum and the energy flux. 

It is interesting to consider the flux of energ>' along a tube of energy 
flow in a steady field. Such a tube may be bounded by two neighboring 
equipotential surfaces of electrostatic potential and two equipotential 
surfaces of magnetic potential. If we consider a short length of such a 
tube then it will, in general, be curved. The flow of energy along it 



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Na'x?^^'*J ELECTROMAGNETIC MOMENTUM. IJ 

and the associated momentum therefore change in direction as the field 
moves along the tube. There must therefore be a force on the tube at 
right angles to its length sufficient to produce the change in the direction 
of the momentum. The Maxwell stresses in a steady field give no 
resultant force on any element of volume free from charge. The stresses 
perpendicular to the tube are the Maxwell stresses but along the tube 
the true stress X' is less than the Maxwell stress X, We have seen that 
X' — qv + X-gv — E. The pressure in the direction of the tube of 
energy flow is therefore less than the Maxwell pressure by qv. There 
will therefore be a transverse force on the tube equal to gvjR per unit 
volume, where R is the radius of curvature of the tube. This force will 
be directed towards the center of curvature. This force is of just the 
right amount required to keep the flux of energy along the tube for it is 
equal to the momentum times the velocity divided by R just as the 
force required to keep a particle of mass m on a circular path is mi^/R. 

Consider again the case of a moving charged parallel plate condenser. 
First suppose it is moving in a direction perpendicular to its plates with 
velocity F. The energy flux between the plates and the velocity of the 
field are both zero. Thus the plate ahead continually generates new 
electric field behind it as it moves along and the plate behind continually 
absorbs the energy from the field. The energy flows from the back plate 
to the front plate through the insulating supports. The velocity of the 
field relative to the plates is — F so that the field goes into one plate 
and comes out of the other. 

If the condenser moves parallel to its plates with velocity V then 
h = Vd/c so that the velocity v of the field is equal to 



E If? 

= - - V-T - C2 = F. 



V 




NB 



Fig. 1. 



Thus the field moves along with the plates which seems a reasonable 
conclusion. 

Now consider the case of a charged sphere moving with a small velocity 
V along a straight line AB. Let the center of the sphere be at (Fig. i) 



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28 H, A. WILSON. ]^SSS1 

at a point P if OP 



H, A. 


WILSON, 


r and POB 


= ^ we have 


-;.• 


eVsin^ 



so that the velocity of the field v is given by v = £:A/d = F sin ^ suid is 
directed along PN. Thus if OJV represents V then PiV represents r. 

The velocity of the field relative to the sphere will be got by adding 
— V to r so that it will be represented by PO. That is, the field to an 
observer on the sphere will appear to be coming in towards the center 
of the sphere with a velocity V cos 6, If ^ is greater than t/2 the 
relative velocity is along the radius away from the sphere. Thus the 
field is absorbed by the sphere in front of it and emitted behind. The 
velocity of the field relative to the sphere at the surface of the sphere is 
equal and opposite to the velocity of the surface along the normal. 

Next consider the case of a condenser consisting of two long con- 
centric cylinders with radii a and b. Let the charge on the inside cylinder 
be e per cm. of length along the axis and suppose that the condenser 
is moving with a velocity V in the direction of its axis. There is then a 
convection current eV carried by the inner cylinder and a current — eV 
carried by the outer cylinder. The magnetic intensity between the 
cylinders will be equal to eV/2Trc at a distance r from the axis. The 
radial electric intensity will be equal to e/2irr. The velocity of the 
field is therefore, since d and h are perpendicular to each other and 
h <d, given by 

eV 2vr 

v = cX X — = F, 

2Trrc e 

so that the field moves along with the condenser as was to be expected. 
The velocity v is equal to C/e, where C = eV denotes the current. If ^ 
denotes the potential difference between the cylinders then 

e = 2T0/log bja 



so that 



,=_£_Iogj/a. 



In the case of two concentric cylindrical conductors with a current C 
flowing along the inner one and a current — C along the outer one the 
magnetic and electric fields between the cylinders are the same as in 
the. case of the moving condensers so the velocity of the field will be the 
same. The flow of energy between the cylinders is in either case equal 
to C0 so that the momentum in the field is equal to C0/c* per unit length 
along the axis. If V is small so that the magnetic energy can be neglected 
compared with the electric then since the electrostatic energy per cm. 



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Na"i^^^*] ELECTROMAGNETIC MOMENTUM. 29 

is equal to ie^ the flow of energy due to convection is equal to ^e<l>V or 
iC<l> so that half the energy is convected and half transmitted by the 
working of the stress in the field. 

In the case of the condenser there is a backward flow of energy in the 
cylinders equal to ^e<l>V due to the tension along them so that the total 
flux of energy along the axis is ^e<l>V as it evidently must be. 

In the case of the concentric conductors at rest there is no backward 
flow and the total flow is C0. In this case the velocity of the center of 
mass of the energy is evidently /C^/^e^ = 2C/e where / is the length 
of the conductors so that the momentum due to energy flux is given by 

(^ ^ e ^ c^ " c« 

or C4>/c* per unit length as before. In the case of the condenser the 
momentum is only \C4>llc^ because half the energy flows back along the 
cylinders. 
^ When the current is first started in the conductors they will receive an 
impulse in the negative direction due to the generation of this momentum 
in the field. This impulse is due to the field existing at the end where the 
current is started before it gets to the other end. The pressure due to 
the field therefore acts at one end for a short time before it is balanced 
by the equal pressure at the other end. 

An analogous case in mechanics can be easily imagined. Suppose we 
have a long closed box with a machine gun in the box at one end. If the 
gun starts firing along the box the box will receive an impuke which will 
last until the bullets begin to strike the other end. The box will there- 
fore move backwards if it is free to move as long as the gun continues to 
fire and will be stopped shortly after the gun stops firing. 

Consider now the case of a condenser consisting of two long con- 
centric cylinders when a uniform magnetic field is generated parallel to 
the axis. The momentum per unit volume between the cylinders in 
this case is he/2Trc so that the total angular momentum in the field per 
unit length along the axis is (6* — a^)he/2c where b and a are the radii of 
the cylinders. While the field is being generated the cylinders are acted 
on by a couple due to the induced electric intensity which gives them 
angular momentum equal but opposite to that generated in the field. 

This case offers a possibility of testing the theory of electromagnetic 
momentum experimentally. A cylindrical condenser with its axis 
vertical could be suspended by a fibre so that it could rotate. The out- 
side cylinder could be closed at each eild and the inner one given a static 
charge. The condenser could be suspended inside a solenoid to produce 



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30 ^. ^- WILSON, ^SS 

the magnetic field. The condenser should be deflected when the mag- 
netic field is produced. If however the force (i/c){d/di)[d'h] is trans- 
mitted through the field to the charges on the cylinders instead of gen- 
erating momentum in the field then no deflection would be obtained. 
The eff"ect to be expected in such an experiment is very small but might 
possibly be detected with a well designed app>aratus. 

If we regard all momentum as due to energy flux then we might 
expect all energy to be subject to gravitational attraction. This idea 
has been confirmed by the recent discovery of the deflection of light 
when passing by the sun. The momentum M in the light is finite so 
that the transverse mass which is equal at any velocity to M/v is also 
finite but the longitudinal mass is equal to Jlf(i — v^/c^)"^ and so should 
be infinite for light. This means that a force acting on light in the 
direction of motion should not increase the velocity of the light but 
should merely increase the momentum and energy in the same proportion 
so that V = Mc^/S remains constant. We should therefore expect the 
gravitational force of the sun to change the direction of light but no^ 
its velocity. Of course Einstein's theory gives a change of velocity 
but it is based on the idea that the gravitational field distorts space. 

If energy is subject to gravitation then various effects must exist 
which are unfortunately probably too small to be detected. For example 
suppose electrical energy is transmitted from a battery through a wire 
of small resistance to a higher level where it is converted into heat in a 
resistance R. Let C denote the current and E the electromotive force 
of the battery. Then we have 

EC= OR+ aRgh/c\ 

where g denotes the acceleration due to gravity and h the difference of 
level. Thus the resistance will apparently be R(i + ghjd) instead of R, 
It h = 10,000 meters the increase in R is about one in 10^*. 

Again in a circuit composed of two metals if one junction is at a higher 
level than the other we should expect a small electromotive force even 
when the two junctions are at the same temperature. This electromotive 
force should be approximately equal to Pgh/c^ where P denotes the 
Peltier coefficient. 

The work done against gravity in transmitting 10,000 kilowatts up 

10,000 meters is about 100 ergs per second. 

The Ricb Institutb. 
Houston, Texas, 
February, 1920. 



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Vol, XVI.i 
No. I. J 



QUANTUM EMISSION PHENOMENA. 



31 



QUANTUM EMISSION PHENOMENA IN RADIATION. 

By David L. Webster. 

Synopsis. 

Comparison of X-rays and Light; a Summery. — This covers the best, known 
cases of excitation of line spectra by electron impact, and the form of the Bohr theory, 
that is required by them. 

Comparison of Emission and Absorption. — The above phenomena are com- 
pared .with corresponding absorption phenomena, with especial reference to the 
accumulation of energy for photoelectrons by absorption. 

Deductions, — Theories of the type of Bohr*s appears inconsistent with these facts. 
The phenomena suggest that the law of the conservation of energy, as applied to 
atomic oscillators, holds only statistically, A set of postulates to replace it for individual 
oscillators is outlined. 

Comparison of X-Rays and Light. 

nPHE purpose of this paper is. to compare the quantum phenomena 

-^ in X-rays and light and to draw conclusions from them on the 

laws governing the emitting mechanism. Let us consider first the simpler 






-K--*t 



fe^ 



'"mue nmmhrs 



L^ series 



^ M "dJ -iU 



zsn. 






jy » 



L^ senes 



■A/ w ^a ^4 "g z: 



i^ 






M 



2c 



Jj^^ £t^ series 



nar- 



idi ULf .111 uy 



^ ? 
^1 A 



Sid 



Fig. 1. 

case of X-rays. In Fig. i, we have the spectrum of platinum, on a scale 
of wave numbers, showing the K, L and M series. In the K series we 



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32 



DAVID L. WEBSTER. 



rSBCOND 

LSbrxss. 



have the strong a lines, the weaker /3 and 7 lines and the absorption 
limit -4. This point A is especially important, because waves of a higher 
frequency than A are absorbed by the element much more strongly than 
those of lower frequency, and also the higher frequency waves give rise 
to a fluorescence consisting of the K series emission lines. If now we 
subject a piece of platinum to cathode rays, we should find no K series 
emission from it unless the energy of a single cathode ray is as large 
as a quantum of the frequency A. (This has not been tested directly 
for platinum, but has been for other elements,* and we may be sure they 
all act the same.) For any higher value of the cathode ray energy, we 






^' 3jf.,3h^i»iimmm 






<^<i/r L 



^.Snr itf 



-/e-T7F 



«Ui/S>^ 



LSvMS 



mJ^^ma/Mnt a 



•ICrc^' , *r T92.00 vlU. 

Fig. 2a. 

have all the K series lines emitted with constant intensity ratios under 

all conditions. Evidently the mechanism used in the production of K 

series rays by cathode rays is such as to demand the same energy quantum 

as that used in fluorescence, and presumably it is the same mechanism.^ 

In the L series we have a similar state of aff"airs, except that the series 

must be divided into three or four sub-series, each with its own absorption 

> For rhodium see D. L. Webster, Phys. Rev., 7. 599-613, June, 1916. For molybdenum 
and palladium see B. A. Wooten, Phys. Rev., 13, 71-86, Jan., 1919. 
« D. L. Webster, I.e. 



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Vol. XVI 

No. I. 



QUANTUM EMISSION PHENOMENA. 



33 



limit and corresponding critical potential. The exact status of the series 
marked Lz and L4 in the diagram is not settled, but Li and Lt are defi- 
nitely known to behave exactly like the K series as shown by evidence 
described elsewhere.^ In every case the energy required is represented 
by many thousands of volts. 

In light, however, conditions are different. For example, in sodium 
vapor, studied by Tate and Foote,* if the energy of the bombarding 
electrons is gradually increased there is no radiation till we reach 2.1 






1 1 

-tIm-- 



Tl 



|T1T 

ilJ I 

I I 1 1 

j I I I I 



WW 

I I 



IILL J 



1 1 
iiii 



Ml' I 

III 
i ' ' ' ' ' 



vmk/? 



-t^ 






^^•^ ASS 



^y^js^ 



Fig. 2&. 



volts, when the well-known D lines appear, alone, as a so-called ''single- 
line spectrum." Now 2.1 volts corresponds exactly to the quantum of 
their frequency. But they are the first lines of a series, like the K a 
lines; and the limit of the series, corresponding to the point A, is at a 

» D. L. Webster and H. Clark, Proc. Nat. Acad., j, 181-5, March, 1917, and D. L. Webster, 
ttrid., Jan., igao. 

« J. T. Tate and P. D. Foote. Phil. Mag., j<J. 64-75. July, 1918. 



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34 DAVID L. WEBSTER. ^SS 

frequency more than twice as high. The D lines are the lines 1.55-2P, 
and the limit, 1.55, corresponds to a voltage of 5.1 volts. When this 
voltage is reached, we get the whole series 1.55^-wP, and with it the sub- 
ordinate series, some of whose lines have lower frequencies than the D 
lines'. The important difference from the X-ray case is the existence of 
the so-called "single-line spectrum," at voltages between 2.1 and 5.1 
volts. Such a phenomenon is unknown in X-rays. 

Now this difference between the two cases is readily explained by 
the diagram in Fig. 2. According to Kossel's^ modification of the Bohr 
theory, the K series is produced by removing an electron from the 
innermost ring, called the K ring, and allowing one to fall into its place 
from another ring, the L, M or N. While I think there is ample evidence 
against the idea that the Bohr rings actually exist, it may be that the 
stable positions that do exist will act in much the same way. I have 
therefore drawn the diagram giving the K position at the bottom, indicat- 
ing that a potential of 78,200 volts is required to lift the electron from 
it to the surface of the atom, where its energy would be zero. The 
energy required to do this is the quantum of the absorption limit, A, of 
the K series. Similarly the energies required to lift an electron from the 
Li and L2 positions are the quanta of the absorption limits Ai and At 
respectively; and the K a lines are produced by removing an electron 
from the K position to infinity and replacing it by one falling from Li 
or L2. By such considerations Bohr* predicted the fact that the critical 
potential for emission of the K series would be that which gives an electron 
a quantum of the frequency ^4, and Kossel, in 1914, predicted the relation 
VKa = vka ■" ^LA which hc tested as accurately as he could, and he also 
predicted some relations between emission line frequencies. An essential 
point for this explanation of the critical potential by Bohr and Kossel 
is that the electron removed from the K position must go to infinity, and 
cannot be allowed to come to rest in the L or M positions. That is, in 
the normal atom all positions involved in X-ray processes are full, . 

In light, on the other hand, we have a set of stable positions, shown 
in Fig. 2 as 1.55, 2P, 2.55, 3P, 3Z>, etc., and the process of exciting the 
single line spectrum is evidently to lift an electron from 1.55 to 2P 
and let it fall back. If the electron is lifted to infinity, or zero energy, 
we shall excite the whole system, including the subordinate series. As 
van der BijP has suggested, the existence of the *' single-line spectrum" 
means simply that in the normal atom no position is filled above 1.5 S. 

> W. Kossel, Verh. d. D. Phys. Ges.. Nov. 30, 19 14. 
«N. Bohr, Phil. Mag., 26, 1-25. July. 1913. 

» H. J. van der Bijl, Phys. Rev., 10, 546-556. Nov., 191 7. Van der Bijl does not call 
i t the 1.55 ring, but describes it in terms equivalent to that. 



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Vol. XVI. 
No. X. 



QUANTUM EMISSION PHENOMENA. 



35 



In mercury, which has been studied by Frank and Hertz, McLennan 
and Henderson, Davis and Goucher and others, we have a more complex 
state of affairs indicated in Fig. 3. The lines i.55-2/>i and 1.55-2P 
both appear at the potentials given by the quantum law, applied to their 



\ 



tu 



tz 



Wi 



f-v*- 



=:feE=- 



-::~j:±---r- 



is;!S- 



{ i I ij 



JT- 



IF 



11, 






r-T-: 









I 

I 



I 









TTTTTTI 



J nil 



•< 

I 



respective frequencies, and the whole spectrum appears at the potential 
given by the quantum of 1.55. Again the explanation is van der Bijl's 
hypothesis that 1.55 is the only position that is normally full. In 
calcium also, effects exactly like those in mercury have recently been 



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36 DAVID JL WEBSTER, [^S2! 

observed by Mohler, Foote and Stimson/ and the explanation is again 
van der Bijl's hypothesis. These phenomena in light show clearly the 
existence of empty positions of stability, and if such empty positions 
were present in the X-ray mechanism they ought to show in the same 
way, by a "single-line spectrum" in each X-ray series. The fact that 
such a single line spectrum fails to occur is therefore strong evidence 
against any theory of X-rays that assumes empty positions of stability 
in the normal atom below the 1.55 position, as several of the recent 
theories do. 

Comparison of Emission and Absorption. 

So far the theory is good, and these elements are typical of the groups 
whose quantum emission phenomena are best known. When we apply 
the theory to absorption, referring again to Fig. 2, we see to some extent 
why it is possible to have sodium vapor absorb the D lines, and lift 
its electron to 2P, and why it is impossible for any element to show 
selective absorption for any of its X-ray emission lines. Instead, it must 
absorb rays above the frequency A, since a quantum of such a frequency 
is required to remove the electron to a place where it can stay. But 
then the question arises, why can not the same process occur in light, 
and why does not sodium vapor absorb not only the D lines but also all 
frequencies above 1.55, and give a fluorescent spectrum under such 
conditions similar to X-ray fluorescence? Applied to absorption, this 
type of theory is most unsatisfactory. 

A more fundamental difficulty appears when we consider the nature 
of the absorption process. The electron must in some way collect energy 
enough from the X-rays to appear as a photoelectron. This, according 
to Barkla,* means the amount h{v + va), where v is the frequency of the 
rays absorbed and va is that of the absorption limit. This conclusion is 
drawn from the observed fractions of the total X-ray energy that appear 
in photoelectrons and in fluorescent X-rays and the fact that the photo- 
electrons all appear to have the same energy, hv. While the evidence 
on this latter point does not seem quite conclusive, it is significant that 
the energy h{v + va) is exactly the amount suggested by the Bohr 
theory, although Barkla's evidence was not drawn at all from this theory. 
I say ''suggested," rather than "required," because it is not certain that 
the electron could not be helped out of the atom by another electron 
falling in from an outer stable position as the first one goes out, thus 
neutralizing the force that would otherwise restrain the one that leaves. 

» F. L. Mohler, P. D. Foote and H. F. Stimson, Bull. Bur. Stan., 1920. Abstract in Phys. 
Rev.. 14, 534, Dec., 1919. 

« C. G. Barkla. Proc. Roy. Soc., A.p2, 501-4. Aug., 1916. 



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No^x?^^^'] QUANTUM EMISSION PHENOMENA. ^J 

However that may be, the electron leaves with energy of the order of 
hv and must collect from somewhere a quantity of this order or perhaps 
h{v + va)' MiUikan* has recently described experiments leading to 
conclusions of the same general type for photoelectrons produced by light. 
Now where does the electron get this energy? If in light or X-rays 
the energy is all concentrated in a point of the wave front, the electron 
might get at once as much as the energy hv of the primary cathode ray, 
but no more. But energy is the ability to do work; and to produce 
co5rdinated motions of electrons in different parts of a crystal, a train 
of waves of X-rays must have this ability at points widely scattered over 
the wave front and perpendicular to it. And in a reflected or scattered 
train of waves the whole energy is very much less than the quantum 
emitted from the primary radiator, according to any reasonable theory 
of these phenomena, so that the amount of energy coming within reach 
of any one atom exposed to this beam must be correspondingly reduced. 
In light, as shown by the diffraction pattern at the focus of a high-power 
microscope objective, the ability to do work must be distributed over 
practically a whole hemisphere of the wave front if not more, thus indi- 
cating a distribution of energy in light even wider than any we have 
definite evidence of in X-rays. It would be most imreasonable to assume 
that X-ray waves are not constructed like those of light, and probably 
the energy is distributed as widely in one case as in the other. If now 
the X-rays have passed through a slit, the wave train thus limited con- 
tains but a small fraction of a quantum, and if they are then reflected 
from a crystal it contains even less. The same is true of light subjected 
to such treatment. But in either case the photoelectron has as much 
energy when produced by the weakest beam as when produced by the 
strongest. And in X-rays photoelectrons can be obtained easily, as 
shown by ionization methods, when the heads of the successive wave 
trains are as far apart, on the average, as many millions of wave-lengths. 
One might perhaps attempt to explain the accumulation of energy by 
the coincidence of a large number of wave trains. But it is well known 
that this would not lead to a photoelectric current proportional to the 
intensity of the rays; and so it is evident that the absorption of energy 
by the photoelectron is not dependent upon coincidence. If not, then 
it must be by a process of gradual accumulation. According to the 
electromagnetic theory it would be very gradual indeed and, even in a 
strong monochromatic beam a resonating electron should take many 
weeks to acquire the energy hv. But aside from such theoretical con- 
siderations, the practical reasons given here seem sufficient to show 
the gradual nature of the process. 

* R. A. Millikan, Am. Phys. Soc. meeting, Dec. 31, 1919. 



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38 DAVID L. WEBSTER. [llSSS 

Now let US suppose an electron from the K ring is absorbing X-ra3r8 
and has lifted itself half way to the position of zero energy, and then is 
struck by a cathode ray. One would expect that if the cathode ray has 
only energy enough to lift the electron the rest of the way to the surface, 
it will produce the K series lines. But no. It must have a whole 
quantum of the critical frequency and no less. The same difficulty 
appears also in light, as one may see by reference to the phenomena 
described above. 

In such a theory as I have just described there seems to be no way to 
distinguish the energy stored by absorption from the energy acquired 
from a cathode ray, and prevent them from being combined as suggested 
above. In a theory of heatradiation that I proposed in 1915,^ based on 
Parson's magneton theory, the distinction might be made, because the 
energy accumulated by absorption was stored in a rotary form not 
readily affected by the impact of a cathode ray. But even here, there 
is some difficulty. The X-ray absorption spectrum is continuous, and 
it is hard to see how we can avoid the assumption that the natural 
absorption frequency of an electron is different at different times. Cer- 
tainly it is not fixed by Bohr's energy considerations, because a larger 
quantum than hvA could not be collected continuously: the electron 
would escape as soon as it has the energy hvA* Some other determining 
factor must be present. In light also, in solids and liquids, especially 
metals with free electrons, there must be continual changes and re- 
adjustments of the electron's frequency. 

If now such a change of frequency occurs when an electron has nearly 
finished collecting a quantum, and the change is to a lower frequency, 
for which the energy already stored is more than a quantum, one would 
expect photoelectric action even if no rays happen to be falling on the 
electron when the change occurs. In this or some such way, one would 
expect some evidence of the stored energy to appear. Thus the magneton 
hypothesis, while distinctly better than the other, is still unsatisfactory, 
because evidence of stored energy fails to appear. The stored energy 
causes trouble, and perhaps more trouble than it is worth. 

After all, what is it worth? As Poincar6* has said, every time we deal 
with a new type of phenomenon, we find or invent a new quantity that 
we can call energy, and define it so as to make the total energy of the 
system a constant. As both he and Ritz* have said, the law of the con- 
servation of energy is not a law, but a postulate. Some time, a phe- 

* D. L. Webster, Proc. Amer. Acad., 30, 131-145, Jan., 191 5; see also Phys. Rbv.. 8, 66-9, 
July, 1916. 

« H. Poincar^, Science and Hypothesis. Paris, 1901, Chapter VIII. 

» W. RiU, Ann. Chim. Phys.. XIII. 145-275. or Collected Works. Paris. 19". P- 345- 



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No*!?^^^*] QUANTUM EMISSION PHENOMENA, 39 

nomenon may arise where this postulate is not advantageous in its most 
complete form. It seems to me that this time has come. Explanations 
of phenomena are important, but a postulate is not. 

To preserve our explanations of refraction and other classical phe- 
nomena of physical optics, let us assume as « usual that the oscillator is 
governed by an equation of the form 

m£ + gx +fx = e£„ 

X being the displacement of the electron from its equilibrium position 
and Eg the external electric force in the x direction. As Ritz suggested, 
a vibration controlled by a magnetic field or some similar agency is more 
probable than the elastic force fx, but as this is the usual form of dis- 
persion equation, we may use it here. Any magnetic or similar vibration 
could be substituted without changing our present conclusions. This 
equation gives absorption at a rate gs?, the mean value of which through 

g 
a whole period is — 17 where U is the energy of the oscillation. Now, 
tn 

instead of assuming this absorbed energy to be stored somewhere, and 
reSmitted some time later, let us assume it to be simply annihilated. 
Then let us assume that the electron may at any time start an emitting 
oscillation of large amplitude, continuing uniformly until a whole quan- 
tum is radiated, or else emit a photoelectron with a quantum of energy. 
And let us assume that the probability of starting such an oscillation or 
photoelectron during a time dt is 

-> 

m Q 

where Q is the ''accumulated energy" defined above, which may \>e hv 
or may be something larger. Further let us assume that transfers of 
energy either to or from cathode rays or other colliding particles can 
take place, but by quanta only. 

That these hypotheses give a mathematical theory of dispersion 
exactly like the classical theory is evident from the fact that the dis- 
persion theory is not concerned witfi what becomes of the power gd^ 
after it is taken from the electron by the damping force. 

To make them give a theory of heat radiation we need only an entropy 
condition for the oscillator. To get this we may use almost the same 
condition as in my heat radiation theory, referred to above, which was 
modelled to a great extent on Planck's. It Q == hv^ the behavior of an 
oscillator in a given field of radiation is almost equivalent to what is 
assumed there, because the rate of absorption and mean rate of emission 



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40 DAVID L. WEBSTER. ^Sm. 

are the same. To make them exactly equivalent, we have only to assume 
that an oscillator newly formed in an atomic readjustment will behave 
almost exactly like the one of the other theory, which absorbed energy 
continuously and stored it, radiating by quanta or multiples of quanta. 
The only difference is that in starting its career with its new fre- 
quency it must not start at the zero of the scale of absorbed energy, but 
at any point on it, the probability of starting at any one point being 
proportional to the density of oscillators on the scale of energy at that 
point; and when it changes frequency again it must not be considered 
to have a store of energy in it. In other words, the stored energy of the 
previous theory must have been merely a mathematical fiction and should 
not have been assumed to have any real physical existence. 

If the energy Q is greater than hv we have a case of fluorescence, the 
energy hv appearing in a photoelectron and the rest as fluorescent rays. 
In this case we get into the question of the thermodynamics of fluorescent 
bodies, which needs a long discussion. In the absence of very definite 
evidence on the exact value of Q, as suggested above, the time does not 
seem ripe for such a theory. 

Summary. 

We may summarize these conclusions as follows: The simple Bohr 
theory is good for explaining the phenomena of excitation of X-rays and 
light by impact, if we assume that in the normal atom all rings are full 
from the K ring to the 1.55 ring, inclusive, but none outside 1.55. But 
the theory is quite unsatisfactory for absorption phenomena. Even if 
the absorbing electron is not a member of a Bohr ring, but a "magneton" 
of the type assumed in my previous theory, situated in a stable position 
similar to a Bohr ring, and having the required resonance frequency, 
there are still some difficulties when the frequency is subject Jo change 
with time. Consequently it seems better to assume that in postulating 
the existence of stored energy in the oscillator we have carried the postu- 
late of conservation of energy a step too far. We had better abandon 
it at this point and postulate a system of equations that give the con- 
servation of energy as a statistical effect only and preserve the explana- 
tions of dispersion and heat radiation intact, at the same time explaining 
the phenomena of excitation of radiation by impact. 

Rogers Laboratory of Physics. 

Massachusetts Institute of Technology, 
Cambridge, Mass. 



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nSTi^^'*] ionization potentials, 41 



IONIZATION POTENTIALS OF ARGON, NITROGEN, CARBON 

MONOXIDE, HELIUM, HYDROGEN AND MERCURY 

AND IODINE VAPORS. 

By Clifton G. Found. 

Synopsis. 

Measurement of the lonitation potential of Gases was accomplished by means of 
a two electrode tube, by determining the point on the current-voltage curve at 
which the current increases at a rate faster than that given by Langmuir's equation 

f -A(K + Ko)*^. 

The effect of a voltage drop along the cathode was eliminated by a commutator ar- 
rangement which broke the filament heating circuit while the electron current 
was being measured. 

The initial velocity of the electrons, Ko. was determined directly from the current- 
voltage curve. 

lonitation potentials were obtained by measurement as follows: Argon 15.6, nitro- 
gen 15.8, carbon monoxide 15.0, hydrogen 15.1, helium 30.5, mercury vapor lo.i, 
iodine vapor 8.5. The ionization potential of argon was found to be constant for 
pressures between i and 200 bars. 

Introduction. 
TT has been sho^m by Langmuir* that for a pure electron discharge, 
-^ when the electrons start from the cathode with zero velocity, the 
maximum current which will pass to the anode is given by 

i = A P^ (i) 

where V is the voltage on the anode and i4 is a constant, depending 
only on the geometry oi the tube. 

The limitation of current is caused by space charge or the negative 
electrostatic field due to the electrons in the space between the electrodes. 
If in any way the effect of this negative space charge is neutralized, the 
current to the anode will increase with the voltage faster than the rate 
given by equation i. One way of neutralizing space charge is by the 
presence of positive ions. Hence, if an electron tube contains gas, as 
soon as positive ions are produced, the current increases more rapidly 
with increase of voltage, causing a point of discontinuity in the volt- 
ampere characteristic curve. 

The voltage at which this kink occurs is a measure of the ionization 
potential of the contained gas. 

» Physical Review, Vol. 11, No. 6, Dec., 1913. 



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42 CLIFTON G. FOUND. ^SS*! 

In the above reasoning, it was assumed that the electrons started \Hth 
zero velocity, but in practice they are emitted with an initial velocity. 
If the average initial velocity is equal to a voltage Vo, then equation 
(i) becomes 

i^A(v+Voy'K (2) 

Thus a voltage must be added to the observed voltage at which the kink 
occurs in order to obtain the true ionization potential. Tate and Foote,^ 
Foote and Mohler* and others have determined the ionization potentials 
of a number of metallic vapors from the position of the kink in the volt- 
ampere characteristic curve. The value of Vq they determined from 
measurements of resonance potentials. 

The present method differs from that of Tate and Foote in that the 
ionization potential in this case is determined directly from equation (2) 
which does not hold rigorously for their arrangement. The facts that 
there was a difference of potential between the end of the cathode due 
to the heating current and also that a third electrode at a voltage negative 
to the anode was present, would prevent the current increasing, at low 
voltages, at a rate as high as that given by equation (2). 

In order to eliminate the effect of a voltage drop along the filament, 
the present measurements were made with a rotating commutator. The 
diagram of connections is shown in Fig. i. The rotating commutator is 



Fig. 1. 

Diagram of electric connections for measuring the volt-ampere characteristics of vacuum 
tubes by use of rotating commutator. 

so connected that no current can flow to the anode while the heating 

current is passing through the filament and the anode current is measured 

during the interval the heating circuit is broken. The speed of the com- 

1 Phil. Mag.. 36. 1918. 

« Phil. Mag., J7, Jan., 1919. 



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No*!^^] IONIZATION POTENTIALS. 43 

mutator is so great that there is no appreciable cooling of the filament 
during the intervals in which the heating current is off. The voltage of 
the anode and the anode current were measured on direct current instru- 
ments. Since these were on only a portion of the time, the readings 
obtained were average values and in order to obtain effective values, it 
is necessary to multiply the observed values by a constant — corresponding 
to the reciprocal of the fraction of the time during which current flowed. 
This constant was determined by taking the ratio of the voltage with 
commutator stopped, to the voltage reading with commutator running. 

In all cases, the values given in the tables are effective values, obtained 
from the observed values by multiplying by the commutator constant. 
This varied from 2.18 to 2.22. The variation was due to resetting of the 
commutator brushes and in no case was a variation found during any 
series of measurements. 

The electron tube which was used for these measurements consisted* 
of two tungsten filaments, each wound in the form of a double helix, and 
molybdenum cylinder about 12 mm. diameter and 12 mm. long. The 
helices and cylinder were arranged coaxially. The inner helix, which was 
5 turns of 0.125 mm. wire wound on a 2.25 mm. mandrel, was used as 
cathode. The outer helix, which had 3 turns of 0.125 mm. wire wound 
on 3.65 mm. mandrel, was connected to the molybdenum, cylinder 
and the combination was made the anode. This arrangement has the 
advantage that the electrons travel from the outer helix to the cylinder 
with a uniform velocity equivalent to the anode voltage so that when 
ionization takes place a larger number of positive ions is formed than if 
the outer helix were not present. 

Since most of the positive ions travel to the cathode, a larger number 
is present in the region between the helices than would be present if the 
electrons did not travel over a large portion of their path with the maxi- 
mum velocity corresponding to the anode voltage. 

Calculation of Ionization Potential. 

To determine the ionization potential of a gas, the volt-ampere char- 
acteristic of the tube was first taken with a goo^ vacuum (about .001 
bars), while it was still connected to a Langmuir condensation pump. 
The tube was then shut off from the pump by means of a mercury trap 
separated from the former by a liquid air trap and a known pressure 
of the gas let in. The characteristics were then taken again with the 
gas present. 

The value of Vo was calculated from equation (2). If ti and t2 are 
the electron currents at two voltages Vi and Vt respectively, below the 



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46 CLIFTON G. FOUND, 

The first vertical column gives the effective values of anode voltage raised 
to the three-halves power. Table II. gives the difference between the 
electron current in a good vacuum and that when gas is present. 

Figure 2 gives the plot between the electron current and the effective 



Fig. 2. 

voltage raised to the three-halves power. It will be noted that the curve 
for a good vacuum is linear throughout the entire range while the curves 
when gas is present are linear only up to a certain point, above which 
the current increases faster than the linear relation. The curves for 
pressures from i to 280 bars apparently begin to depart from a straight 
line at the same point and the rate of departure increases with the pres- 
sure. At the lower pressures, it is difficult to tell the exact point at which 
the departure commences, but at the higher pressures the curve when gas 
is present meets that for a good vacuum at a sharp angle and there is no 
doubt where the effect of ionization sets in. For this reason, a high 
pressure of gas was used to determine the ionization potentials of the 
other gases. 

Table III. contains the results for nitrogen. The first column gives 
the three-halves power of the effective voltage. The second and third 



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Vot. XVI. 
No. I. 



•] 



IONIZATION POTENTIALS, 



47 



give the corresponding values of the electron current with gas present 
and in a good vacuum, while the last column gives the difference between 
columns two and three. Figure 3 shows plot of results with nitrogen. 

Table III. 

Nitrogen, 



P (Ban) . . .' 


300 
1.6 
1.14 


.001 

I.X 

1. 00 




Ko (Volts) 




/...!?.........::. 








(K+ro)»/« 


Ki 


' 


A* 


4.45 


.35 


-.31 


.04 


10.9 


.76 


.74 


.02 


18.8 


1.36 


1.29 


.07 


28.0 


1.96 


1.92 


.04 


38.6 


2.65 


2.68 


-.03 


50.5 


3.40 


3.43 


-.03 


53 


3.60 


3.64 


-.04 


56 


4.00 


3.84 


.16 


59.5 


4.20 


4.08 


.12 


63 


4.45 


4.32 


.13 


66 


5.10 


4.52 


.58 


69 


6.50 


4.74 


1.76 


73 


8.40 


5.00 


3.40 


76 


11.6 


5.20 


6.40 



Ionization potential ■■ (63)*'* or 15.8 volts. 



« 1- 


f 


^ tiAll'ItiA^ 










i 


^^ it 


t t 


A j: 


T ^ ^dL 


Jt ^ ^^ 


i -,^ 


^i tr*^ 


t j^^ 


^ y 


^ 


^ 


^ ^^ 


^ y 




^ ^^ * 


^ .7 V •*? 


A^, S9 S7 4f ^' ^^ " -' »> AH 



Fig. 3. 



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48 



CLIFTON G. FOUND, 



Tables IV., V., VI., VII., VIII. give the results for carbon monoxide, 
hydrogen, helium, mercury vapor and iodine vapor respectively, while 
Figs- 4» 5t 6» 7 and 8 give the corresponding curves. 

Table IV. 

Carbon Monoxide. 



P (Bmri) 


aoo 
a.a 
x.03 


.001 

x.x 
x.oo 




Vq (Volti) 




H V *«.»«/ 








(F+Ko)»/« 


Ki 


1 


Ax 


6.0 
12.9 
21.5 
31 

42 

51 
54 
58 
61 
64 

67 

74 
81 


.51 
1.14 
1.90 
2.80 
3.65 

4.55 
4.85 
5.10 
6.00 
8.20 

12.00 

20.6 

32.0 


.57 
1.19 
1.96 
2.80 
3.68 

4.55 
4.85 
5.10 
5.40 
5.55 

5.82 
6.60 
7.38 


-.06 
-.05 
-.06 
.00 
-,03 

.00 
.00 
.00 
.60 
2.65 

6.18 
14.0 
24.6 



Ionization potential « (58)*^» or 15. volts. 



■^ 




o 


/? 


Qt 


Vk 


/K 


U 


vr 


Xi 


/? 


c* 




■-t— 




— 




— 


— 






%M 


IM4 






mmd 




• 


ftjl 
























»A» 


f*m 


>404 




v« 


' r 


► 












-■ 












































































f 
























' 




















































» 


1 






















4 
















? 






















1 














> 


\ 






















/ 






>^ 










\ 






















/ 


1 


/ 










^ 


\ 






















i 


/ 




















































2 




















,j 


r 


































^ 




































/ 




































V 




































/ 


































/ 


r'' 


























* 








./ 


/ 


































/ 


p 


































v^ 




































^ 












C" 


r¥i 


;• 




















z 


/ 


r 


/ 


9 


/ 


9 


4 


t 


/ 


» 


i 


' 


/? 


a 


? 


i 


9 


A f 



Fig. 4. 



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Vol. XVI.I 
No. I. J 



IONIZATION POTENTIALS, 



49 



Table V. 

Hydrogen. 



P (Bart) , , 
j^ (Voltt) 

6.8 
13.7 
22.0 
31.5 
40 



135 
x.a 



A7 



48 
54 
57 
60 
63 

65 
68 
73 
86 



.38 
1.00 
1.58 
2.23 
2.75 

3.35 
3.78 
4.01 
4.22 
4.45 

4.70 
5.10 
5.63 
8.00 



.001 
X.I 

x.oo 




I 


A/ 


.48 


.10 


.95 


-.05 


1.52 


• .06 


2.18 


.05 


2.75 


.00 


3.32 


.03 


3.74 


.04 


3.96 


.05 


4.17 


.05 


4.38 


.07 


4.52 


.18 


4.72 
5.06 


.38 
.57 



2.08 



Ionization potential « (59)«'» or 15.1 volts. 



^ 


— 


~ 














— 












-"■ 




— 


— 


^ 








































/ 


// 










m 


7? 


?r, 


^, 


""/I 


f 


















1 












l¥»d 




!•«- 


> ** 


'fl 


>«<M 




jf 


























fJ94 


Mtf 


W^ 


hr 4 


««. 


wm 


ti' 


'iZ 


tavr 


}»c* 


)^^ 






1 


































r"* 






-f- 

1 




^ 










































































/ 






^ 


? 
































/ 








; 






























1 


















































j 




























/ 








y 




\ 




























/ 




/ 


y' 
































/ 




y 










•* 
























O 


> 


y 


































J 


i^ 














^ 






















mA 


> 




































^ 






































> 




































/ 


^ 
























p 












^ 




































y 


^'1 




































/ 














ir 






















,^ 


/• 












» 


»y 


p 




















^L 


^' 


9 


/ 


9 


J 


9 


_4\ 


?-A 


4 


9 


4 


7 


7 


9 


s 


? 


_s 


u 


/* 



Fig. 5. 



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50 



CLIFTON G. FOUND. 



ISbcomd 
LSbrzbs. 



Table VI. 

Helium. 



/'(Ban) 


650 
2.2 
1.60 


VacttoiB 
2.2 
1. 00 




^0 (Volte) 




A-.... _::::::::. 








(K-fFo)«'« 


Ki 


1 


Ai 






6 


.123 


.176 


-.53 


13 


.220 


.275 


-.55 


21.5 


.358 


.385 


-.27 


31.1 


.520 


.530 


-.10 


42 


.700 


.700 


.00 


54 


.91 


.900 


.10 


67 


1.12 


1.12 


.00 


74 


1.28 


1.23 


.05 


81 


1.47 


1.36 


.11 


88 


1.68 


1.50 


.18 


96 


1.95 


1.60 


.35 


103 


2.47 


1.74 


.73 


112 


3.10 


1.85 


1.25 


120 


3.68 


1.96 


1.72 



Ionization potential — (94)'/* or 20.5. 



Fig. 6. 



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No. z. J 



IONIZATION POTENTIALS. 



51 



Table VII. 

Mercury Vapor. 



PCBtuM) 


3.0 
a.75 
a.o 


.001 
3.3 
1.0 




Kj'CVote) 




x^.,T^...^.^. 








(^+ Ko)»/t 


Ki 


' 


A/ 


4.6 


.84 


.84 


.00 


11.2 


2.15 


2.15 


.00 


15 


2.75 


2.85 


-.10 


19.4 


3.63 


3.74 


-.11 


24.0 


4.45 


4.55 


-.10 


26.5 


5.20 


5.20 


.00 


29 


5.80 


5.60 


.20 


32 


6.20 


6.10 


.10 


33 


6.65 


6.40 


.25 


34 


7.20 


6.50 


.70 


35 


8.20 


6.70 


1.50 


36 


9.50 


6.85 


2.65 


37 


11.0 


7.09 


3.91 



Ionization potential * (32)*^* or 10.1 volts. 









































rfl 












































































Jlf 










/ 


ff 


^t 


// 


9[ 


" i 


^1 


=v; 


fl» 


























OM 


MM 








rr1 


Lm 






















c 


*** 


r» ' 


«# 




r/m 


;;^ 


5r^ 


vn 


• ^, 


r/»K 


^Mf0 


■ 






































-\ 




jf 












































































m 








































I 




































M 


\ 
































y 






5 
































/ 


^ 




i 






























1 




< 




1 






























/ 


^ 




4 


{ 




























V 


«^ 






■^" 


\ 


























r 


/ 








^ 


■r 
























^ 


































1 


X 


































/ 


/^ 


































^ 




































y 


































/ 


^' 


































^ 




































/ 




































/ 


































y 


4 












\f ^ 




1^ 


















^ 








/ 


2J 




— T 




-4 


? 




^ 




^ 


L- 






^^ 



Fig. 7. 



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52 



CLIFTON G. FOUND, 



rSBCOND 

LSbeibs. 



Table VIII. 

Iodine Vapor, 



PCBtcn) 


40 
.35 

2.5 


.OOI 

1.6 

I.O 




Ko' (Volte) 


, 


A-.-Tr^.. .:::::::. 








(K+Ko)«/t 


Kt 


1 


M 






4.3 


.35 


.32 


.03 


10.9 


.78 


.77 


.01 


19.4 


1.44 


1.45 


-.01 


24.2 


1.80 


1.80 


.00 


25.0 


1.90 


1.87 


.03 


26.1 


2.00 


1.95 


.05 


27.2 


2.10 


2.03 


.07 


28.2 


2.30 


2.10 


.20 


29.5 


2.40 


2.25 


.15 


30.5 


2.54 


2.32 


.22 


31.5 


2.77 


2.40 


.37 


32.6 


3.25 


2.48 


.77 


33.5 


3.75 


2.57 


1.18 


37.0 


5.25 


2.80 


2.45 



lonlKition potential « (aS)*/' or 8.5 volts. 











"~~ 








— 






— 


— 













n 


~~ 






































T 




if 




































f 








































/ 








































/ 














TC 


Oi 


Ni 


c- 1 


^ 


^ 


^ 




























'vu 


•M»t 


'/*f 


"* 


y« 


}^a 




fet 


*% 














_£ 










tAm 




tt0A 
ttU 


#-« 


r^«c 




\z 


?% 


r^. 




'^ 




















































\ 








































\ 








































\ 






































Jt 


\ 








































\ 




































/ 




I 




























/ 




y 


/' 






\ 




























r 


/ 










5 




























\/ 










t 


^ 
























/ 














*• 
























/ 


\ 




































/ 




































V 


V" 




































y 




































\ 


/ 


























*" 










y 


y 




































^ 


• 


































/\ 


y 
















jf 




















y 


< 














(f-i 


4 


* 


















^ 








' 











z 











J 


9 








y. 



Fig. 8. 



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No^i?^^] IONIZATION POTENTIALS. 53 

The curve for helium shows two Idnks, the first one at 16.5 volts and 
the second at about 20 volts. One explanation that might be given for 
these results is that helium has two types of ionization, a weak one occur- 
ring at 16.5 volts and a more intense one at 20 volts. Since no other 
experimenter has found ionization in helium as low as 16.5 volts, it 
seems more probable that this value is due to a slight impurity in the 
helium, although the latter was purified by passing through charcoal 
at the temperature of liquid air. The helium used was known to contain 
a slight admixture of neon, which would not be removed, as it passed 
through the charcoal at the temperature of liquid air. Since it would 
require only about 6 bars or i per cent, of neon to account for the magni- 
tude of the kink at 16.5 volts, it seems very probable that this kink is 
due to ionization of the neon content, while the ionization potential of 
helium is given by the second kink at 20.5 volts. 

Summary. 

1. It has been shown that the relation* 

holds for the electron tube used in these experiments when no gas is 
present. 

2. When gas is present, the above relation holds up to a certain voltage 
corresponding to the ionization potential of the gas, beyond which the 
ciurent increases at a faster rate than given by the equation. 

3. From the location of the point of departure from the above relation, 
the ionization potentials given in Table IX. were determined. 

Table IX. 

Gftt. loniatioii PotentiaL 

Argon 15.6 

Nitrogen 15.8 

Carbon Monoxide 15.0 

Hydrogen 15.1 

Helium 20.5 

Mercury vapor 10.1 

Iodine vapor 8.5 

In conclusion, the writer wishes to express his appreciation of the kindly 

interest taken in these experiments by Dr. Langmuir, whose suggestions 

proved most valuable. 

Research Laboratory, 
General Electric Co., 
Schenectady. N. Y. 



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54 ^^- TERZAGHI, [ggS 



NEW FACTS ABOUT SURFACE-FRICTION. 

By Ch. Tbrzaghi. 

Synopsis. 

Friction between Smooth Surfaces: Physical Properties of Clays, — In the present 
paper the author discusses a number of preliminary experiments leading to an 
investigation of the phsrsical properties of clays. Since plastic deformations of 
clay-bodies involve the sliding of the smooth clay particles upon each other, in 
order to determine the character and the laws governing the frictional forces, the 
author studies the behavior of smooth glass plates placed in contact under different 
conditions of loading. As a result of these experiments it is established that the fric- 
tional resistance between two surfaces is not due to the shearing strength of a cushion 
of air or water; but to the existence of microscopic particles that deposit themselves 
on the rubbing surfaces. Frictional resistance was found to be independent of the 
thickness of the air cushion. 

Properties of Very Thin Layers of Water; Permeability and Water Contents of 
Clays, — ^A drop of water was placed between two glass plates and was allowed to 
evaporate. When the thickness of the lasrer of water was reduced to about lOO /im« 
the evaporation stopped completely, suggesting that the molecules of a solid are able 
to exert forces over distances of the order of 50/1^. Such thin layers of water 
have, beside viscosity, shearing and tensile strength. The author uses this result 
to explain the facts: (i) that layers of clay are impermeable unless the head exceeds 
a certain minimum; (2) that the water contents of cla}rs do not drop below a certain 
limit; (3) that a drop of water does not spread over a surface wetted by water. 

Theory of Surface Friction. — ^As a result of the observations mentioned and of a 
new set of experiments, the author concludes that the ordinary laws of friction of 
rest apply only where contact between the rubbing surfaces must be enforced by 
outside pressure. When two even surfaces are in contact the explanation of the 
causes of friction is not so simple on account of the presence of small particles on 
the surfaces. 

THE following article may be considered as a preliminary report on 
a series of investigations carried out by the author in the Labora- 
tories of Robert College, Constantinople (Branch institution of iV^. Y. 
State University). 

I. Introduction. 

Most of the properties of clays, as well as the physical causes of those 
few properties that have been investigated, are unknown. We know 
nothing about the elasticity of clays, or the conditions that determine 
their water capacity, or the relations between their water content and 
their viscosity, or the earth pressure that they exert and not even about 
the physical causes of the swelling of wetted clays. As a consequence 



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Na"x?^^*] ^^^ PACTS ABOUT SURFACE FRICTION. 55 

the civil engineer, dealing with this important material, is at the mercy of 
some unreliable empirical rules, and laboratory work carried out with 
clays leads only to a mass of incoherent facts. In order to establish a 
reliable theoretical basis for his practical investigations, the author has 
endeavored to solve the following questions: Is it possible to explain the 
physical properties of clays by means of the ordinary laws of physics 
(surface friction as a force, proportional to the surface pressure, acting 
merely in tangential direction, the laws of capillarity and the law of 
Darcy) or are we obliged to modify these laws in their application to the 
physics of colloidal matter? 

II. Surface Friction between Bodies with Smooth Surfaces. 

Microscopical examination of clays shows that clay consists of a loose 
mass of small, transparent bodies with more or less smooth surfaces. 
Every plastic deformation of a clay-body involves the sliding of such 
surfaces on each other. No process can better be compared with this 
phenomenon than the sliding of two glass-plates on each other. But 
the question arises, as to whether the sliding of glass-plates on each 
other takes place under the same physical conditions as the relative 
motion of two grains of clay, and if not, what is the essential difference 
between the two cases of friction? The dealing with this fundamental 
question has forced the author to a new conception of the physical causes 
of friction of rest. This conception is evolved as a natural consequence 
of the following experiments: 

1. A glass-plate with an even surface was laid on .the table and covered 
by another one of the same size and quality. The surface of contact 
showed next to one of the comers a green spot surrounded by Newton's 
rings, the rest of the surface remained colorless. By pressing the colored 
spot with a glass-stick the color of the center became a yellow of the 
first order, indicating a thickness of 140 mai (0.00014 mm.) for the air 
cushion separating the two sheets, no further approach of the two glass 
plates being possible. The observation revealed the fact that the original 
green color of the center was of the fifth order corresponding to a distance 
of more than i /i (o.ooi mm.) and that this distance represented the 
minimum distance between the two bodies in unloaded condition. The 
experiment has been very often repeated, but the coloration and the 
location of the colored spot was always different, the only fact in common 
to the observed phenomena was the fact, that the minimum distance 
between the two plates never dropped below i fi. 

2. Two square glass-plates of 2 x 2 cm., 0.15 mm. thick, were provided 
with a system of fine scratches. The average width of these scratches 



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56 CH. TERZAGHI, [^JS? 

was 0.2 /x. By means of these scratches a map has been plotted of the 
air cushion separating the two sheets. The minimum distance between 
the sheets was found to be 3.7 /*, the maximum distance 32 ju. This 
experiment too was several times repeated, always with approximately 
the same result, but the spot of minimum distance changing its location. 

3. Thirty four of the above-mentioned square glass-plates were placed 
one upon the other, so that they formed a prism of a total weight of 4.3 gr. 
This prism was placed under the microscope and gradually loaded up to 
a total load of 100 gr. The first application of the load resulted in a 
permanent settlement of 3 /i per glass-sheet. At each new application 
the permanent settlement became smaller and finally the prism assumed 
the character of a perfectly elastic body whose modulus of elasticity 
increased rapidly with the load. By increasing the load from 2.85 gr. 
to 23 gr. per cm.*, the total average compression was measured to be 
4.17 /x per sheet. The same experiment was repeated with the glass- 
sheets placed under water. The result of the loading test was practically 
the same, with the only difference, that an increase of the load from 2.85 
to 23 gr. resulted in a compression of 4.85 /x per sheet. In both cases 
the application of additional load was immediately followed by de- 
formation. 

The following experiments were devoted to an endeavor to find out 
the nature of the force that prevents the glass-sheets from touching. 
If the two glass-sheets were separated by an air or water cushion only, 
experiment No. 2 would have shown that: 

(a) The thickness of the cushion would decrease with increasing load. 

{b) The frictional resistance between the two surfaces would be due 
to the shearing strength of the cushion; and as experience shows that 
frictional resistance increases in approximately direct proportion with 
the load we would have to conclude: 

{c) That the shearing strength of a cushion of given area increases 
with decreasing thickness. 

4. Two glass-prisms with particularly smooth surfaces were placed 
one above the other and the frictional resistance between the two bodies 
was directly measured by means of an accurate balance. After each 
experiment, the two surfaces were carefully rubbed with b, cloth and 
freed from dust with a camel-hair brush. The distance between the 
two surfaces was indicated by the visible interference effect and varied 
between the very wide limits of 0.6 and more than 1.2 /x. Frictional 
resistance was found to be independent of the thickness of the air cushion. 

5. The same prisms were placed 2 cm. below the surface of distilled 



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Ko*'i^^^*] ^^^ FACTS ABOUT SURFACE FRICTION, 57 

water. Increase of water pressure up to 30 cm. did not effect their 
mutual distance. The third and fourth experiment show that the thick 
air and water cushions observed in the first and second experiment 
cannot be considered as the seat of the forces that keep the surfaces 
apart. The spacing was afterwards found to be produced by bodies of 
microscopical size, enclosed between the two surfaces. It must be simply 
considered as a statistical law, similar to the laws that determine the 
death-rate and the number of suicides in cities, that, as soon as a surface 
is exposed to air or water, a certain number of small fragments attach 
themselves to it and the dimensions of the three biggest particles deter- 
mine distance as well as frictional resistance. That must be considered 
as the cause why there does not exist any definite coefficient of friction 
between glass and glass. The angle of friction varies between the limits 
of I® and 10® and the case of friction at moderate pressure between the 
smooth surfaces of two bodies which are not separated by a third, one 
cannot be realized except in microscopical dimensions. 

6. A glass sheet of 2 x 2 cm., 0.15 mm. thick was fixed to the upper 
surface of a glass plate of bigger dimensions by means of a drop of water 
enclosed between the two bodies. The temperature in the room being 
28® C. the water evaporated rapidly until several wet spots remained, 
surrounded by Newton's rings. The thickness of the water-cushion 
could be estimated to be about 100 fifi. A great number of such couples 
were produced in a similar way and the result was always the same. 
Several water spots have been systematically examined under the micro- 
scope for enclosed microscopical bodies and typographical maps have 
been plotted indicating position and dimension of every obstacle. In 
every water spot a certain number of fine crystal-leaves could be located, 
but while in most of the spots the leaves were simply enclosed between 
the two surfaces, in one spot two particles have been discovered indicating 
by their coloration, that they stood under very high pressure. Simul- 
taneous evaporation tests have been carried on. Water with its surface 
2 cm. below the upper edge of a narrow glass-tube evaporated with a 
rate of about i mm. per day. A water surface 8 cm. below the top of 
a similar tube went down with a rate of about 0.3 mm. per day, while 
the water spots between the glass-sheets did not show any measurable 
sign of evaporation, even those which joined the outer edge of the glass- 
sheet, even although they have been purposely exposed for several days 
to the sun and to the wind. 

The results of this experiment indicate clearly, that a water-cushion 
of less than 100 mm has properties which are different from the properties 
of larger bodies of water. The low rate of evaporation can be explained 



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58 CH. TERZAGHI. [g^S 

in two different ways; Either the surface of the edge of the waterspot 
is covered by a layer of saturated vapor that is kept from diffusion by 
molecular attraction through the molecules of the solid body, or the 
water-molecules are kept in their position by the same forces- But if 
the molecules of the solid body are able to act over a distance of more 
than 50 fifjL on the rapidly travelling molecules of saturated vapor, the 
more they will exercise their solidifying influence on the quieter molecules 
of water within the same range of distance. The distance of 50 mm is 
identical with the distance (measured by Quincke)^ up to which glass 
is able to influence the angle of contact between water and silver. 

Combining the result of experiment No. 6 with the fact (observed by 
Seelheim and discussed by Forchheimer)* that layers of clay are imper- 
meable unless the head exceeds a certain minimum, which is a fimction 
of the thickness of the layer, we are now obliged to attribute to the 
surface layer both the qualities of a solid and of a liquid, at least in the 
case where such surfaces meet each other between the surfaces of two 
solid bodies. This involves within the film of the liquid not only viscosity 
but shearing- and tensile-strength too. 

The double thickness o.i m of the contact-layer is the approximate 
width of voids in a thickly packed mass of grains whose size is smaller 
than I or 2 fi. According to Atterberg* no powder with uniform size 
of grains shows plasticity unless its particles are smaller than 2 fi. 

Experiment No. 6 explains the fact, observed by the author, that the 
water content of a clay exposed to the air at ordinary temperature does 
not drop below a certain limit ranging between 4 and 8 per cent, of the 
weight of the dry matter (the exact value depending on the size and 
particularly on the shape of the grains). 

The fact that the influence of the molecules of the solid body is exerted 
up to a distance of more than 50 fifi from the surface seems to bear a 
relation with the unexplained fact, that a drop of water does not spread 
over a surface wetted by the water, but that its surface sloi>es down to the 
surface on which it rests, forming with it a certain angle of contact. If 
the influence of the molecules of the solid body were limited to a distance 
equal to the thickness of the surface layer of the liquid (0.06 /x/i), the 
mentioned effect would not be possible as a simple statical consideration 
shows. The author explains the phenomenon as follows: The surface 
layer of the waterdrop is not anchored to the surface AB of the glass- 
sheet (Fig. i) but to the semi-solid surface layer ABCD and is therefore 
unable to spread because the area of this layer is limited. Another 

^ Annales de Chimie et de Physique. 

* Ztsch. d. Ver. d. Ing., 1901. 

• International reports on pedology, 1913. 



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No*?^^*] ^^^ PACTS ABOUT SURFACE FRICTION, 59 

simple experiment made with an eye-glass and a wet handkerchief 
indicated too the semi-solid character of thin films of water. Sweeping 
the handkerchief over the glass, the glass surface was covered with a thin 
film of liquid showing interference-colors. The surface of drops of 
water placed upon this film formed with it an angle of contact just as 

[O.otm* •ur.f»c«-l«y«r of liquid. 




SOuM, aurfiLCA-iftyttr of contact . 

Fig. 1. 

they would do it they were immediately placed on the glass surface, 
they showed no tendency to spread and their behavior was not at all 
influenced by the gradual evaporation of the film that surrounded them. 
While the film itself did not contract to drops as a thicker film would do 
but it retained its original relief until it evaporated. 

III. Elastic Theory of Surface-Friction of Rest. 

Under the influence of the results of his observations the author 
assumes that surface-friction stands in direct proportion to the area 
of those parts of their surfaces which are closer to each other than o.i /i 
(called area of contact) and distinguishes three different cases of friction : 

Case (a). Very Smooth and Even Surface ^ Low Surface-Pressure, — 
The action is transmitted by intermediate bodies of microscopical size 
(Fig. 2, a). The area of surface of contact is, according to the formulas 

Bdharent' mleroacopic 
Cat* to 



area of contact 



Fig. 2. 

of Hertz, smaller the smaller the radius of curvature at the place of 
contact. Hence, as the shape of the intermediate bodies is a matter 
of chance, the coefficient of friction is extremely variable. 



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60 CH, TERZAGHL [ISSSS 

Case (b) Very Smooth and Even Surfaces^ High Surface Pressure (Fig. 
2, b), — ^The intermediate bodies disappear in depressions produced above 
and underneath them by high local pressure. The surfaces of the two 
main-bodies come in contact, the radius of curvature of this surface is 
by far bigger than the radius of curvature of the surfaces of the micro- 
scopical bodies, and the coefficient of friction goes rapidly up. With 
increasing pressure the peripheral parts BB of the surfaces whose radius 
of curvature is still greater than that of the central part A come in contact, 
the coefficient of friction increases therefore furthermore, although not 
as rapidly as at the limit between case (a) and case (ft). These assump- 
tions are verified by a series of facts published 1829 by Rennie.^ This 
author found for the coefficient of friction / between' steel and iron at 
different surface-pressures the following values: 

Pressure p = 8.79 kg. cm.,"^/ = 0.166 corresponding to a later stage 

of case (a). 
p = 23.62 kg. cm.r^f = 0.333, earlier stage of case (i). 
With further increasing pressure p he found an increasing/ until he 
obtained for p = 47.25 kg. cm.~*, / = 0.403. 

Experiments carried out with other materials led him to similar 
results indicating that the coefficient of friction rises first rapidly and 
then slowly with increasing pressure. 

Case (c). Bodies with Rough Surfa^^es. — ^The friction is a complicated 
result of the effect of molecular attraction due to contact and of the fact 
that the asperities of the two surfaces stand to each other in a similar 
relation as the teeth of two gears (Fig. 2, c). But as the surface of contact 
is already at the very beginning more considerable than in case (a), 
as it can never reach as big values as in case (b) and as furthermore the 
second element which determines the frictional resistance in case (e:), 
the geometrical form of the two surfaces, is practically independent of 
the pressure, the coefficient of friction is a fairly definite figure and this 
explains the curious fact that the complicated causes of friction between 
rough bodies lead to a simpler effect than the seemingly simple causes of 
friction between two smooth surfaces. 

The indicated theory removes the apparent contradiction between 
the fact of tangential frictional force and the molecular theory of matter. 
As long as the surfaces are in contact they adhere to each other not only 
in tangential direction but in every other direction too. But the adhesion 
perpendicular to the surface cannot be observed because as soon as the 
pressure is relieved the area of contact becomes again nearly zero, the 
surface resuming their original shape and this remark leads to a very 

> Phil. Trans., 1829. 



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Nol^i^^^*] ^^^ FACTS ABOUT SURFACE FRICTION. 6 1 

important conclusion essential for the understanding of the properties 
of clays: 

The ordinary laws of friction of rest are only applicable to the friction 
between bodies whose original surfaces do not fit each other and whose 
contact must be enforced by external pressure. Two bodies joining each 
other with perfectly even surfaces would present not only a lateral resistance 
against displacement but resistance against separation too. 

The latter fact has been demonstrated by the following striking 
experiment: A very dilute solution of a clay, distinguished by the flat 
shape of its particles and very strong Brownian movements was placed 
on a thin sheet of glass, inside a ring of a height of 2 mm. Five minutes 
after having filled the ring, the cylindrical space was covered with a 
glass cover, so that there was no trace of air between the bottom and 
the cover, and the whole was turned upside down. Twelve hours later 
the vessel was turned again, and after another twelve hours top and bot- 
tom were examined under the microscope. All particles smaller than /m 
adhered to the glass cover and all particles bigger than this size stuck 
to the bottom. The colloidal particles showed no trace of Brownian 
movement, apparently kept in their position by molecular forces. Turn- 
ing the vessel upside down again the coarse particles remained in their 
places on the upper surface of the water-body. A drawing was made 
of some characteristic parts of the crystal groups and twelve hours later 
it could be stated that no grain had left the top-cover, a clear proof, 
that in the case of contact without external pressure the retaining forces 
act not only in a horizontal but also in vertical direction. 

The author is deeply indebted to the College and to Mr. Tubini, 
A. M. I. E. E., acting dean of the engineering department of Robert 
College for. very liberal assistance. 
Robert College, 

ROUMELI HiSSAR, 

July I. 1920. 



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62 W, E, PORSYTHE, I|5SS 



rSBcoto 



SPEEDS IN SIGNALING BY THE USE OF LIGHT. 

By W. E. Forsythb. 

Synopsis. 

Relative Length of Dot, Dash and Space for Light Signaling. — ^A preliminary 
investigation was carried out to determine the relative lengths of dot. space and 
da^h necessary for the greatest speed. Three observers made readings for this 
test and all agreed very well with the following ratio for the maximum speed: 
dot : dash : space :: i : 4 : 3. 

Spewed for Sharp Cut-off of Signals. — To test out the speed for a sharp cut-ofif of the 
signals, using this ratio for dot. dash and space, a sector was made with which 
s^ven different signals could be shown. This sector was mounted so that the 
observers saw the light source through a small opening. According to the criterion 
adopted, speeds were obtained that would correspond to 9 to 13 five-letter words per 
minute. 

Speeds of Reading under Various Conditions. — It was shown that different ob- 
servers were able to read the different signals at about the same speed with signals 
that were sharply cut off (as with the sector) and when the signals were made by 
turning on and off a special ribbon laifip filled with argon gas. The speeds of reading 
using other types of lamps were slower than for the ribbon lamp. With the observers 
at a distance and the lamp in a signalling unit, speeds somewhat slower were ob- 
tained. When an observer failed to read a given signal correctly the failure was 
generally due to his inability to see the dots. 

IN connection with the design of some tungsten filament lamps to be 
used for signaling purposes it was found that little if any information 
was available as to the possible speed of signaling using flashes of light. 
This depends on two factors, the inertia of the eye and the characteristics 
of the source used. The purpose of this investigation was to ascertain if 

possible the maximum speed at which signals 
of this kind can be read and to compare this 
speed with those attainable when using certain 
types of tungsten filament signal lamps. 

A preliminary investigation was made to find 

the relative time intervals corresponding to a 

dot, space and dash which would permit of the 

Fig. 1. maximum speed of reading. A disk was made 

Disk with adjustable opaque ^p having a 120° opening and provided with a 

movable opaque sector which rotated with the 

disk (Fig. i) but could be fixed at any position in the opening. The size 

of this sector determined the interval corresponding to a space while its 



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SPEEDS IN SIGNALING BY THE USE OP LIGHT. 



63 



position defined the relative intervals for the dot and the dash. The 
speed of the disk was measured by a speedometer. 

This disk was mounted between a lamp and a small opening (1.5 mm. 
in diameter) in front of which was placed a shutter controlled by a 
telegraphic key and relay, the latter connected with a commutator 
attached to the disk shaft. With the disk rotating, the shutter opened 
when the operator pressed a key, whereupon the observer, sitting about 
4 meters in front of the opening, saw flashes of light of different duration 
with an intervening period of darkness and then the shutter closed. In 
this way a given signal was seen only once but by properly adjusting the 
position of the opaque sector it was possible to show any one of three 
signals, i.e., dot space dash, dash space dot, or dash alone. Using a 
given size of sector and a given ratio of dot to dash interval, a number 
of these signals given in irregular order were presented for successively 
increasing speeds of the disk until a speed was reached beyond which 
they could no longer be differentiated. Then using the same sector, 
the ratio of the dot and dash intervals was changed and another series 
of readings was made until the maximum speed was reached. From the 
data thus obtained a curve was plotted with the ratio of dash to dot as 
abscissa and for ordinate the reciprocal of the time required to see the 




Fig. 2. 

complete signal when the disk was rotated at a maximum speed. The 
procedure was repeated for a series of seven different sized opaque sectors, 
subtending angles of 10°, 15°, 20°, 30"*, 45**, 60°, 80** and thus a family of 
curves was obtained as shown in Fig. 2. They represent the observations 
of a single observer, and show that for this observer and under the given 
conditions a ratio of dash to dot of approximately 4 to i corresponded to 
the maximum speed of reading for most of the sectors and particularly 
for the 45® sector. Moreover the speed using the latter sector was greater 



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64 W' E. FORSYTHE. [sm^. 

than that obtained with the 30° on the one hand or the 60° on the other, 
and hence the correct size of sector for the greatest attainable speed would 
seem to be in the neighborhood of 45°. This corresponds to a propor- 
tionality of dot : dash : space :: i : 4 : 3. Later, a like test by another 
observer gave results slightly different from those shown in Fig. 2. The 
maximum speed when the movable sector was 45° occurred for a ratio 
of dot to dash of about i : 4 as in the first test. In this second test, 
observations were made with a 52>^° sector and the value for the maxi- 
mum speed was about equal to that for the 45° sector, with the difference 
in this case, however, that the ratio of dot to dash for maximum speed 
was about i : 9, which gives I : 8 : 9 as the proportionality for dot, 
space and dash. 

This second test seemed to show that about the same maximum speed 
would be obtained for the sectors above 45® up to 80** out of 120, with the 
difference, however, that there was a very great increase in the ratio of 
dot to dash for the very large sectors. 

It is well known that in the case of any incandescent electric lamp a 
time interval elapses after the current is turned on before the filament 
glows with full brilliancy, and similarly time is required for the glow to 
disappear after the current has been cut off. If it were possible to con- 
struct a lamp in which full brilliancy and complete absence of glow were 
synchronous with the closing and opening of the circuit it would be 
possible to study the part played by the eye in determining the maximum 
speed of signaling independent of the characteristic of the lamp. Such a 
limiting case can be almost exactly reproduced by the use of a disk with 
proper openings rotating in front of a very small opening before a con- 
tinuously luminous source. The relative time intervals for dot dash 
and space found in the preliminary investigation evidently apply rigor- 
ously only to this limiting case, and it should be noted that while the 
use of this proportionality for any signal lamp is an assumption, it is 
probably not far from right and applies to all of the data to be subse- 
quently presented. 

In the main experiment the first procedure was designed to ascertain 
the maximum speed of signaling for the limiting case, and to compare 
this with that obtained when the flashes were produced directly by a 
type of signal lamp which other experiments indicated would give the 
greatest speed. The previously mentioned disk might have been used 
for this purpose but in order to have a greater number and more com- 
plicated signals corresponding more nearly to those used in practice, 
a second disk was constructed using the ratios noted above for dot, dash 
and space. It is illustrated in Fig. 3 and with it the following seven 



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Na*!?^^*] SPEEDS IN SIGNALING BY THE USE OF LIGHT. 65 

signals could be shown (a space of course occurs after each dot and each 
dash) : 

1 dot dash dot dash 

2 dash dot dot dash 

3 dash dot dot 

4 dash dot dash dot 

5 dash dash dot dot 

6 dot dash dash dot 

7 dot dash dash 

This disk was then mounted with respect to the signal lamp in a manner 
quite similar to that described for the disk used in 
the preliminary experiment. The apparatus was so 
arranged that the different signals could be pre- 
sented in any prearranged order while the disk was 
in rotation. The position of the observer and the 
use of the shutter were the same as previously de- 
scribed. A 6-volt, 2-ampere ribbon-filament signal- 
type tungsten lamp was used as a source, and held at *^* 
a color temperature in the neighborhood of 2950° K. ^^^ "^'^^ ^i*'' ^^ 

_, . . r t 1 • t 1 closed spaces to give seven 

The mtensity of the light was so great that a one different signals, 
per cent, transmission screen was interposed to 
make observation more comfortable. The intensity was still ample for 
accurate reading. 

The following method was employed in making a test. A series of 
12 signals arranged in a haphazard order as determined by the playing- 
card method, were presented at each of a series of successively increasing 
speeds of the disk, starting at a point such, that there was no question of 
ability to decide what the signal was. A record was made of all decisions 
and the experiment was continued until a speed was reached at which, 
from the number of errors, it was evident the observer had passed the 
limit of accurate judgment. 

In order to make measurements with the lamp directly, a commutator 
was constructed by means of which the intervals during which current 
was turned on and off were in the same ratio for dot, space and dash as 
the disk-exposure times previously referred to. The relation of dot : 
space : dash is somewhat different in this case than when the sector was 
used. This is due to the fact that it takes a somewhat longer time for 
a lamp to heat up than to cool off. This shortens the dot relative to the 
dash and lengthens the space. From the results of the test for the rela- 
tive length of dot to dash by the second observer, this would make but 
little difference, if any, in the final results. With the disk removed but , 



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66 



W, E. FORSYTHE. 



fSioo 
LSmi 



Other arrangements tHe same, an exactly similar series of readings were 
made as before, using the 12 signals and successively increasing speeds. 
There was practically no resistance in series with the lamp. Each 
observer made runs with both the disk and the lamp, the two series of 
measurements following each other in rapid succession in order to main- 
tain as nearly as possible the same eye conditions. 

The results are shown in Table I. In column one are given the recipro- 
cals of the time in seconds from the beginning to the end of the signal. 
In the succeeding columns are given for each observer the number of 

Table I. 

Results for Disk Compared with those for Ribbon-Filament Tungsten Lamp in Argon, 



Reciprocal of 
Time in Seconds 
from Beginning 


Nnmber of Signali Reed Correctly Oat of die Twelve Signels Shown. 


w.w. 


J.R.C. 


F. B. C. 


Disk. 


Lamp. 


Diak. 


Lamp. 


Diak. 


Lamp. 


.20 


12 

12 

12 

12 

11 

10 

10 

9 

9 

8 

8 

7 

5 

7 

3 

4 


12 

12 

12 

12 

12 

12 

12 

12 

11 

8 

11 

9 

5 

5 

3 

1 


12 

12 

12 

12 

12 

11 

12 

12 

12 

12 

12 

11 

12 

7 

9 

5 

4 


12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
11 
10 
10 
9 
5 



12 

12 

12 

11 

11 

11 

9 

9 

7 

4 

5 

6 

3 

6 

1 




12 


.25 


12 


.30 


12 


.35 


11 


.40 


11 


.45 


10 


.50 


10 


.55 


9 


.60 


7 


.65 


7 


.70 


9 


.75 


3 


.80 


7 


.85 


3 


.90 


5 


.95 


3 


1.00 


4 



The results for W.W. indicate a breakdown at about the point .50 which corresponds to a 
speed of about 9 five-letter words per minute. 

For J.R.C. the breakdown point would be at about .80 which corresponds to a speed of 
13 five-letter words per minute. 

The results are arrived at by allowing two mistakes out of the twelve signals shown. 

signals read correctly out of the 12 presented at each speed, both when 
the disk was used and when the lamp was used directly with the commu- 
tator. The data show very little if any difference on the average between 
the results using the disk and those using the lamp and indicate that the 
eye and not the lamp was the limiting factor in the speed of reading the 
signals. 
, Having found that the special gas-filled ribbon-filament timgsten lamp 



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Vol. XVLI 
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SPEEDS IN SIGNALING BY THE USE OP LIGHT, 



67 



used gave results as good as those obtained by the use of the disk, it 
seemed desirable to compare this lamp with other equivalent types such 
as a lamp with a ribbon filament, in a vacuum, and also a gas-filled wire- 
filament lamp. The previous tests were all carried out in the laboratory 
where the observer was insured plenty of light and sharp contrast and 
had no difficulty in locating the flash. In order to carry on the tests 
under conditions more nearly like those which occur in practice, the 
lamp and commutator apparatus were moved up to the roof of the 
laboratory. The effect of distance between the observer and the appa- 
ratus was simulated by setting up the lamp without a reflector so that 
the observer saw the flash, against the sky as a background, with an inten- 
sity such as to give a flux equivalent to that which would be obtained 
by the use of the regular reflecting apparatus with the observer 20 or 30 
times as far away. The procedure as to number and order of signals 
and speeds was the same as before. In the first test comparison was 
made with a lamp having a ribbon filament of the same shape but in a 
vacuum. The lamps were oriented so that the intensity in the direction 
of the observer was the same for each. For this run the observer was 
stationed at a distance of 100 yards and the results, given in the second 
and third columns of Table II. indicate that the gas-filled lamp is best 
for this work. A comparison was then made of the gas-filled tungsten- 

Table II. 



Comparison hehoeen a Gas-fiUed Ribbon Lamp and a Vacuum Ribbon Lamp; also between a 
Ribbon Lamp and a Wire Lamp, both Gas-fiUed, 




Nnmber of Sigoftli RMd Correctly Out of die Twelre Signali Shown. 


RedprooU of Time 
in secoadt from 
Bogimiiiig to End. 

of SfCDftl. 


W.W. 


J.R.C. 


w. 


w. 


K.M. 


Gae- 
fllled 
Ribbon! 
Lamp. 


Vecunm 
Lamp. 


Gaa- 

flUed 

Ribbon 

Lamp.s 


Gaa- 
fllled 
Wire 
Lamp. 


Gas- 

illled 
Ribbon 
Lamp.> 


Gas- 
filled 
Wire 
Lamp. 


Gas- 

filled 
Ribbon 
Lamp.* 


Gaa- 
filled 
Wire 
Lamp. 


.20 


12 

12 

12 

12 

11 

12 

9 

8 

5 

6 

3 


12 
12 
11 
8 
8 
7 
7 
6 
2 


12 

12 

12 

11 

9 

6 

7 


12 

11 

12 

6 

8 


12 

12 

12 

12 

9 

8 

8 

7 

5 


12 

12 

11 

11 

9 

6 

7 


12 
12 
12 
10 
8 


10 


.25 


11 


.30 


5 


.35 




.40 




.45 




.50 




.55 




.60 




.65 




.70 





» Distance of observer 100 yards. 
* Distance of observer 170 yards. 



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68 



W. E. FORSYTHE, 



rSaooMO 
ISvRns. 



ribbon lamp and a gas-filled tungsten-wire lamp using 'three observers 
at a distance of 170 yards. The former lamp was run at a color tempera- 
jture of abou* 3000** K. and the latter at about 3100** K. As before the 
lamps were oriented so as- to have approximately the same intensity in 
the direction of observation, and the results indicate superiority for the 
ribbon type. As operated for the most part in this test there was some 

Table III. 

Determination of Speed of Signalling under Various Atmospherical Conditions and at a Dis- 
tance of 2,700 Yards with a Gas-filled ribbon^fUament tungHen signal lamp mounted in a 
Standard Housing with a Reflector. 



Rtciprocal of 
Time m Seconds 



From Beginning 
)f Signal. 



toBndof I 



Number of Signals Read Coirectly Out of the Twelve Signals Siiown. 



Results of W.W. 



.15. 
.20. 
.25. 
.30. 
.35. 
.40. 
.45. 
.50. 
.55. 
.60. 
.65. 
.70. 
.75. 



11 

12 

12 

11 

12 

12 

9 

11 

7 

8 

5 

5 

7 







12 


10 








12 


12 


12 


12 


12 


11 


11 


12 


11 


11 


12 


8 


12 


9 


12 


12 


9 


12 


8 


11 


11 


7 


12 


6 


9 




7 


12 


6 


7 




9 


11 


7 


6 




8 


12 


4 


6 






9 


5 


4 
4 








3 


4 









12 

12 

12 

12 

11 

12 

10 

5 

5 

4 



Results of KM. 




1. Cloudy, conditions changing. 

2. Cloudy, some fog. 

3. Cloudy, some fog. 

4. Clear day. 

5. Clear day. 

6. Night. 



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No!"i.^^'*l SPEEDS IN SIGNALING BY THE USE OF LIGHT. 69 

resistance in the lamp circuit. The effect of this should be to lower the 
speed of the lamps. A test to see whether the effect would be appreciable 
and different in the two lamps showed a slowing up in both but a difference 
so small as to be almost within the limits of experimental error. 

To still further reproduce actual practice two observers were placed 
at a distance of 2,700 yards. The gas-filled ribbon lamp was then placed 
in a regular signaling unit which gave about a 5-degree spread. The data 
are recorded in Table III. For observer WW, the limit of speed of 
receiving signals would appear to be lower on foggy days than on clear 
days and highest at night. On the other hand the results of K.M. showed 
little difference on clear or foggy days, but were better at night. 

Assuming a five-letter word, and that the same speed was maintained 
for continuous sending of signals the 0.50 point in column one corresponds 
to about 9 words per minute, and the 0.80 point to about 13 words per 
minute. 

A word might be said regarding the appearance of the signals when the 
speed approached the limit beyond which the signals could not be 
identified. Each observer was instructed to record what he saw, not by 
code letter, but by actually writing down the dots and dashes. A study 
of these records shows that on clear days inability to see initial dots 
caused uncertainty and eventually breakdown, dashes only being seen 
ultimately. At night, owing to the greater. apparent brightness, the 
spaces seemed to vanish and a mere flicker appeared. In this connection 
it should be noted that in night work no red glasses were used such as 
are frequently employed in practice. 
Nela Research Laboratory, 
Cleveland, Ohio, 
March, 1920. 



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70 H. D. ARNOLD. 



PHENOMENA IN OXIDE-COATED FILAMENT 
ELECTRON TUBES. 

• By H. D. Arnold. 

Synopsis. 

Thermionic Phenomena in Wehneli Oxide Electron Tubes, — ^The author discusses 
some of the problems which have arisen in connection with the development of 
three-electrode vacuum tubes with special reference to the production of a highly 
active and uniform thermionic source of electrons. The materials and the methods 
for the preparation of both core and coating are given. Since tubes with these 
filaments are not self-evacuating by the clean-up effect to the extent found with 
tungsten filaments, greater care is necessary in the pumping process. 

Pure Electron Discharge; the Influence of Pressure and of Bombardment by Positive 
Jons, — ^The evidence shows the electron emission from Wehnelt oxides to be purely 
thermionic. Preliminary measurements on the number of electrons emitted from 
these filaments under the bombardment of positive ions prove that no appreciable 
part of their activity can be attributed to this cause. Operation has been studied 
with pressures of the order of io'^<> mm. Hg.. but no decrease in activity is found at 
these low pressures. A plot is given summarizing the constants of Richardson's 
equation for 4,000 filaments. 

Rate of Evaporation of Oxide Coating, — Grams per cm.* per sec. evaporated from 
a filament coated by the above process are approximately given by 

«.-4.6Xio'r-'/«.-i^^. 

Thinly Coated Filaments; Coating by Evaporation, — Preliminary results of work 
now being carried on by Dr. C. J. Davisson show that maximum thermionic activity 
may be reached with coatings considerably less than one molecule deep. This 
suggests that of the two important constants determining electron emission, the 
density of free electrons in the substance and the work function at the surface, 
the latter is modified by the presence of the oxides while the former may remain 

tttially that of the core. 



THE most generally interesting phenomena in electron tubes are 
those relating to the flow of electrons through the space, the control 
of this flow by plate and grid voltages, and the operation of the tubes in 
the various circuits in which they are used. These phenomena are 
essentially the same whether the filament is pure metal or is oxide 
coated, and a considerable literature has already grown up in this field. 
The phenomena distinctive of oxide-coated filament tubes are those 
relating to the economic and scientific factors involved in the process of 
electron emission. I shall therefore confine myself as closely as .possible 
to these factors as they have influenced the design of oxide filament tubes, 



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nSTx?^^'] electron tubes. 71 

and as we have been led to investigate them in connection with our 
development of these tubes during the past seven years. For reference 
to the scientific literature in this field attention is called tp the appended 
bibliography. 

Wehnelt oxide filaments offer the most economical source of electrons 
at present available for use in three-electrode vacuum tubes, and thus 
from a commercial point of view they are at present of the greatest 
interest and importance. On purely scientific grounds they have long 
been of peculiar interest to physicists and chemists, offering as they 
have one of the most promising fields for speculations on the possible 
effect of chemical action in aiding the emission of electrons from hot 
bodies. 

The early work of Richardson, H. A. Wilson, and others, established 
beyond reasonable doubt that for pure metals the emission of electrons 
is due to thermal action and not to chemical action in the ordinary sense 
of the word. Of the early evidence the most convincing was the proof 
that the emission did not decrease as more and more of the residual gas 
was removed, and the proof that the emission did obey the law of varia- 
tion with temperature which would be expected if the effect were purely 
thermal. Further work* showed that the distribution of velocities among 
the emitted electrons was that which would be computed on the basis of 
the equipartition of energy between molecules and free electrons in the 
metal, the faster of the free electrons escaping in spite of the restraining 
influence of an electric field at the surface of the metal. Still other 
experiments* established that the value of this potential difference, as 
determined from the cooling of the metal due to the electron emission, 
corresponded with the value deduced from the observed relation between 
emission current and temperature. In view of these facts physicists 
have believed for the past ten years or more that there was no place for a 
chemical theory of emission as far as pure metals are concerned. 

With respect to Wehnelt oxides, however, there was somewhat less 
certainty as to whether chemical action might not be necessary for 
electron emission. While it is true that early experiments established 
that with oxides as well as with pure metals the emission did not depend 
on the presence of gas in the evacuated chamber, the presence of the 
oxide itself on the filament seemed to offer sufficient chance for chemical 
actions, irrespective of any gas. Moreover, the fact that coating metals 
with these chemical compounds increased their electron emission many 
fold seemed to invite the hypothesis that this increase resulted from 

» Richardson and Brown, Phil. Mag., Vol. XVI., p. 353 (1908). 

* Richardson and Cooke, Phil. Mag., Vol. XXV., p. 624 (1913); Vol. XXVI ., p. 472 (1913) 



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72 H, D. ARNOLD. ^^, 

chemical action, although there has never been any experimental evidence 
clearly requiring such an hypothesis. 

Data similar to those which established the purely thermal nature of 
thermionic emission from metals, were accumulated more slowly in the 
case of Wehnelt oxides, largely because of experimental difficulties which 
were encountered. The determination of the correspondence of the 
work function as obtained from the cooling effect, and as found from the 
exponent in the emission-temperature equation, followed several years 
behind the similar determination for pure metals, this in spite of the 
fact that the earliest experiments with the cooling effect were attempted 
by Wehnelt and Jentzsch^ using Wehnelt oxides. As for the velocity 
distribution among the emitted electrons, this, as far as I am aware, has 
still to be satisfactorily determined for the oxides. Nevertheless, the 
evidence as it has been verified step by step has in every case supported 
the opinion of the physicists who believed that emission from oxides as 
well as metals was in all probability a purely thermal affair and did not 
require any assumption of chemical action for its explanation. 

With the inception of the use of oxide filaments for commercial vacuum 
tubes, we had to face the same difficulties of technique in producing the 
filament that had retarded the scientific experimenters in their work, 
and it was in addition necessary to produce filament in large quantities 
and with a very high degree of uniformity. To do this a survey was 
made of the metals available for the core of the filament, and of the 
materials and methods of coating best adapted to the manufacture of a 
highly active and uniform filament. Considerations of mechanical 
strength, electrical resistance, non-oxidizability, availability and repro- 
ducibility of cornmercial supply, etc., led us to choose for the core a wire 
of platinum-iridium (about six per cent, iridium, with the other impurities 
usually found in commercial platinum-iridium). This wire was rolled 
to a ribbon to increase the surface, and the ribbon was twisted to secure 
a better mechanical structure. This core could be produced in quantity 
with electrical and mechanical properties sufficiently uniform for our 
purpose. 

In the choice of coating materials we had available the oxides of 
barium, strontium, and calcium, with thermionic activities in the order 
given. Experiments with coatings of BaO, however, showed a mechan- 
ical disintegration during life which outweighed in importance its superior 
thermionic activity. Efforts to secure longer life resulted in the use 
of a mixture of BaO and SrO applied in a number of consecutive coatings. 

* Wehnelt and Jentzsch, Verh. der Deutsch. Physik. Ges., lo Jahrg., p. 6io (1908); Ann. 
der Physik. Vol. XXVIII., p. 537 (1909)- 



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Na'i?^'*] ELECTRON TUBES. 73 

In the process which we most commonly used, barium in the form of 
carbonate, and strontium in the form of hydroxide or carbonate, was 
mixed with some carrier such as resin or paraffin, which would burn 
away when heated in the air. In the coating process four applications 
of the strontium mixture were followed by four of the barium mixture, 
and this process was then repeated, making a total of sixteen separate 
applications. After each application the wire was raised momentarily 
to a temperature of about a thousand degrees, which burned away most 
of the organic carrier. When the coating was complete the wire was 
heated to about 1200° for two hours. At the end of this time there 
remains a fairly heavy coat of BaO and SrO (from 2 to 3 milligrams per 
sq. cm. surface), while next to the core is a firmly adhering layer which 
is built up due to chemical reactions between the coating and the core. 
Analysis shows this coating to consist of barium and strontium combined 
with platinum, rhodium and iridium, the compound present in largest 
amoimt being barium platinate (BaPtOs). The compound with rhodium 
seems to be more readily formed, but due to the small percentage of 
rhodium present this compound makes up only a small fraction of the 
total. 

The filament thus formed can be handled without undue precaution 
so long as it is not exposed to moisture or carbon dioxide. When stored 
in vacuum containers it shows no signs of deterioration even after a 
period of several years. 

The time required for the proper evacuation of an oxide filament tube 
is determined almost entirely by the requirement that a large part of 
the occluded gases must be removed from the metal and glass parts 
inside the bulb. In case the metal parts can be heated before assembly, 
or can be heated electrically, either through leads from the outside or by 
Tesla currents, the evacuating process may be very much shortened. 
In any event it is desirable to carry the evacuating process considerably 
further in the case of oxide filament tubes than with tungsten filament 
tubes, since the clean up effect of the filament itself is not nearly so marked 
as is the case with tungsten. 

During the pumping process the filaments are glowed for several 
minutes to liberate any gases they may have occluded. At the same time 
the compounds at the surface of the core decompose to a certain extent, 
as is evidenced by the fact that filaments taken from tubes after a con- 
siderable period of glowing show a marked diminution in the amount of 
BaPtOs and similar compounds. 

With the exercise of proper care as to the purity of the materials used 
and with adherence to a definite schedule of coating and heat treatment, 



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74 B' ^- ARNOLD, [^2S! 

filament can be produced with every expectation of uniformity and long 
life. During the war some half million vacuum tubes were made employ- 
ing this filament, and the filament was prepared as a part of the regular 
manufacturing process by practically unskilled labor. Expert super- 
vision was of course necessary to guard against the intrusion of chemical 
impurities or variations in the coating process. 

We have naturally made a very thorough study of this so-called 
"standard" filament in order to determine its properties and particularly 
the factors which influence it during life. Having been developed in the 
first instance, about seven years ago, to meet the needs of telephone 
repeater service, severe requirements were imposed upon it from the 
start. Tubes made with it are required to be completely interchangeable. 
No adjustment of filament or plate voltages is made when tubes are 
replaced, and no appreciable change in amplification, or in electron 
current, may result from an interchange. The operation of the tube as 
an amplifier must remain unchanged when the filament voltage is varied 
between the limits customarily met with in storage battery service. 
The operation of the tube must remain sensibly unchanged through a 
life of several thousand hours, and when it does fail for any reason, it 
must give suflicient warning to ensure its being removed from service 
without causing the interruption of a telephone conversation. These 
and numerous other requirements are rigorously enforced, making it 
far more diflicult to manufacture tubes for telephone repeater service 
than for the other uses for which they have since been adopted. 

What terminates the useful life of an oxide filament is usually the 
development of local faults or *' bright spots" due to the evaporation 
of the coating. They are practically free from the most common ageing 
effect of pure metal filaments, namely the gradual increase of electrical 
resistance caused by the evaporation of the filament. In the case of 
tungsten filaments used on constant voltage supply evaporation with the 
resulting increase in resistance causes a lowering in the filament tempera- 
ture and therefore a decrease of the electron emission, while with a con- 
stant current supply the increase in resistance results in an increase of 
temperature and a progressive increase in rate of disintegration of the 
filament. With oxide coated filaments it is the coating alone that 
evaporates, at least until a bright spot is formed, and the temperature 
and operating characteristics remain unchanged throughout life on either 
constant current or constant voltage supply. 

The cost of electrons in a vacuum tube device is determined by the 
characteristics of the filament, by the cost of the power used in heating 
the filament, and by the life and the replacement cost of the tube. The 



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NoTx^^^'] ELECTRON TUBES. 75 

physical factors necessary for computing the cost are the constants in 
Richardson's equation, the constants of the evaporation equation, and 
the radiation constant peculiar to the filament. In order to relate the 
life of the tube to the vaporization constants it is necessary in addition 
to know to what extent vaporization may proceed, on the average, before 
the useful life is terminated, and this can, of course, only be arrived 
at by exhaustive life tests. 

For tungsten and molybdenum the physical constants are already 
available, but for Wehnelt oxide filaments these constants have not as 
yet been satisfactorily established. Preliminary results have, however, 
been obtained in our laboratory and Dr. C. J. Davisson is continuing 
the investigation. We have found that the total thermal emissivity 
lies between 0.45 and 0.70, for a considerable number of samples of our 
standard filament. The method followed in determining these limits 
was to get the resistance power relation for the filament under operating 
conditions, and later get the resistance-temperature relation by placing 
the tube in an electric furnace. The latter relation was checked by an 
observation at the melting point of potassium sulphate. In connection 
with measurements of filament temperatures it was found by the use 
of the optical wedge method that these oxides act practically like black 
bodies in the red region of the spectrum and hence the temperature 
can be read with a fair degree of accuracy by means of an optical pyrom- 
eter using the black body calibration. 

The preliminary values of the evaporation constants, obtained by 
evaporating barum oxide from a tungsten boat, catching it on a platinum 
shield, and weighing the deposit show that with a fair approximation 

where m is the rate of evaporation in grams per sq. cm. per second. 
A more definite determination of these constants for BaO, SrO and CaO 
is under way. 

As for the determination of, the constants in Richardson's equation for 
oxide filament, this work has covered about 4,000 filaments, and the 
results are of sufficient interest to warrant more detailed consideration. 
To simplify the investigation of this matter Dr. Davisson has devised a 
form of codrdinate paper in which the coordinates are power supplied 
to the filament (abscissae) and thermionic emission (ordinates). The 
coordinate lines are so disposed and numbered that if the emission from 
a filament satisfies Richardson's relation, and the thermal radiation 
satisfies the Stefan-Boltzmann relation, then points on the chart co- 
ordinating power and emission for such a filament will fall on a straight 



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76 H, D, ARNOLD, [smS 

line. For practical purposes the advantage of replacing temperature 
by power as the independent variable is obvious. From the slope and 
position of a line on this chart together with the area of the filament, 
it is possible to calculate bE^^^ and a£~*'^ where b and a are Richardson's 
constants and E is the total thermal emissivity of the filament. The lines 
shown in Fig. i give some idea of the characteristics of our standard 



Fig. 1. 

filament and the range of variability. Ten per cent, of the filaments 
have a greater activity than that given by the upper line while the 
activity for 90 per cent, of the filaments lies above the lowest line. In 
this connection it should not be overlooked that in the great majority 
of vacuum tube applications we are concerned only in maintaining the 
electron emission at a value greater than a certain fixed limit. It is in 
no way injurious for the emission to exceed this limiting value. In a 
limited number of cases, however, it is desirable to use tubes with as 



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NoTx^'*] ELECTRON TUBES. 77 

nearly as possible the same voltage saturation value of emission. For 
these special problems pure metal filaments offer at present the best 
solution, since the uniformity of their saturation values can be more 
readily maintained. 

The dotted curved lines on the figure are drawn through points of 
constant ratio of emission to power, that is, constant efficiency or econ- 
omy. The customary operating power is from 8 to 9 watts per cm.*, 
so that the range of efficiencies is seen to lie between 10 mils per watt and 
100 mils per watt. Assuming the emissivity of the filament to be 0.6 
we obtain from these lines the following values of thermionic character- 
istics of the filament. 

Equivalent volts through surface ^ = 1.55 to 1.9, 
Richardson's constant 6, 19.4 X 10' to 23.8 X 10', 
Richardson's constant a, (0.5 to 1.5) X 10^ for electrons per sec. per cm.*, 

(8 to 24) X 10* for amps./cm.* 

In our adaptation of Wehnelt oxide coated filaments to commercial 
vacuum devices we have found it desirable in a number of instances to 
carry on investigations which would appear to be more immediately of 
scientific than of commercial value. One of our early experiments which 
was reported by Dr. W. Wilson at the Christmas meeting of the American 
Physical Society in 1914 gave additional data as to the behavior of 
Wehnelt oxide filaments in very high vacuum. The experimental ar- 
rangement used consisted of a cylindrical anode, with suitable guard 
rings, surrounding a single strand of oxide coated filament placed along 
the axis of the cylinder. The vacuum was made as good as possible 
with a Gaede molecular pump and it was established that the electron 
current in the filament did not diminish even with these extreme vacua. 
It was expected that the current would vary with the 3/2 power of the 
voltage according to Child's^ space charge relation and that from the 
coefficient K, which involves among other factors the quantity Ve/m 
we might determine whether the carriers in the case of Wehnelt oxide 
filament were electrons or were in part carriers of greater mass. Wilson 
found that when proper consideration was taken of the geometrical form 
and of the voltage drop along the filament, the space charge equation 
took the form* 



^,i^y- 






•5 V, 

» Child. Phys. Rev., Vol. 32, p. 492 (191 1). 

« See also E. R. Stoekle, Phys. Rev., Vol. VIII., p. 545 (1916). 



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78 H. D. ARNOLD, KSS 

where Vo' is. the potential of the negative end of the filament and Vo 
the potential of the positive end. The value e/m obtained from the 
experimental data by the use of this equation was found under the best 
conditions to be about 5 per cent, lower than the value obtained for 
electrons by other methods. This deviation is explicable either by the 
presence of a very small number of negative carriers of molecular size or 
by the emission of secondary electrons from the anode under the bombard- 
ment of the primary electrons. The deviation is however, no greater 
than that obtained with tungsten filaments, and the concordance of the 
results indicates clearly that the discharge from Wehnelt oxides may be 
considered a pure electron discharge. 

By means of the Knudsen absolute manometer, and later by the use 
of the Buckley ionization manometer,^ we have measured vacua of the 
order of lo"* and io~^® millimeters of mercury during the operation of 
Wehnelt oxide filaments, and have never found any indication of the 
emission current falling off as the vacuum improved. With the intro- 
duction of various gases at pressures of the order of .001 millimeter, or so, 
the electron emission currents do suffer rather large changes, although 
not of the degree found with the emission from tungsten filaments under 
similar conditions. The presence of oxygen and carbon dioxide inhibit 
the electron emission, while a small amount of hydrogen in contact with 
a filament of abnormally low emission may result in restoring it to a 
normal condition. Because of their relatively smaller variations in 
emission under the action of gases we have found Wehnelt oxide filaments 
more adaptable for use in Buckley ionization manometers than pure metal 
filaments, as it is very rare that any blocking effects develop which 
cannot be overcome by a reasonable increase in the filament temperature. 

In another paper* before the Physical Society in April, 191 7, Wilson 
gave the results of a series of experiments on the relation between the 
work function ^ and the exponent b of Richardson's equation. The 
method followed was a modification of that first attempted by Wehnelt 
and Jentzsch for oxide filaments and later used by Richardson and his 
collaborators in investigating the cooling effect due to the emission of 
electrons from filaments of osmium and tungsten. Previous experimen- 
ters who had attempted to determine the cooling effects with Wehnelt 
oxides had found it impossible to get consistent results due to the non- 
uniform behavior of the filament. During Wilson's experiments our 
standard methods of coating were employed, and the results obtained 
were remarkably consistent and reproducible. The values obtained 
were as follows: 

» O. E. Buckley. Proc. Nat. Acad. Sci., 2, 683 (1916). 
« Proc. Nat. Acad. Sci., j, 426 (191 7). 



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Vol. XVI.! 
No. I. J 



ELECTRON TUBES. 



79 



*^//VolU. 



4 Voltt. 



BaO 50 per cent., SrO 50 per cent 

BaO 50 per cent., SrO 25 per cent., CaO 25 per cent. . 
CaO 



ii 



2.02 


1.97 


2.16 


2.28 


2.34 


2.39 


2.59 


2.54 


3.28 


3.22 


3.49 


3.51 



We have recently been repeating some of these experiments with a 
slightly different bridge arrangement and find no difficulty in obtaining 
consistent results from a given filament over long periods of time. 

The close correspondence between b and 0, is as pointed out above, 
one of the grounds for believing that chemical action does not play any 
part in thermionic emission. The correspondence is, of course, not a 
proof of the absence of chemical action, but it is certainly more easily 
explained on the assumption of thermal action than on the assumption 
of chemical action. The determination of > is also of considerable, im- 
portance in connection with the theory of photo-emission and of contact 
potentials. 

In connection with our recent experiments Dr. Davisson is finding it 
of great convenience to use filaments which have been coated by active 
material evaporated from a standard filament. The standard filament 
and the wire to be coated are mounted close together in the same tube 
and the primary is run at a fairly high temperature for various lengths of 
time according to the purpose of the experiment. Observations are then 
made on the emission from the secondary filament. One advantage of 
this method of experimentation is that the core of the secondary filament 
may be any suitable material, for example, tungsten or iron, without 
meeting the difficulties of oxidation, which are often troublesome when 
these materials are coated in the open air. 

These secondary filaments have many interesting properties which no 
doubt will prove of importance in establishing the process of electron 
emission from Wehnelt oxides. One of the most striking facts is that 
the secondary filament may show a high electron emission when only a 
very minute amount of active material has been transferred to it. In 
certain experiments where the secondary filament was tungsten, the 
standard filament was glowed for so short a time that only approximately 
one tenth of the surface of the tungsten filament was covered with active 
material. While we have not determined in just what form the deposit 
comes down on the secondary, it seems reasonable to suppose that the 
material is transferred essentially molecule by molecule, and that the 
surface of the secondary filament would be found to have on it a consider- 



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8o H. D. ARNOLD. IISSS 

able number of single molecules of coating separated by distances of the 
order of one to ten molecular diameters, and in addition a certain number 
of groups of two molecules, a much smaller number of groups of three 
molecules, and so on. It is most interesting to note that the electron 
current obtainable at a given temperature from filament coated in this 
very tenuous fashion may be only a little smaller than that obtained 
when the entire filament is covered with a heavy deposit. 

It is natural to ask whether this result is due to a difference in the a 
or in the b of Richardson's equation as applied to these partly coated 
filaments. Work along this line is not yet completed, but measurements 
of b taken at intervals while the deposit was fornjing have never shown an 
increase with thickness of deposit, and therefore it seems that the result 
must be due to a difference in a. If we assume that a completely coated 
filament emits uniformly over its entire surface, while a partly coated 
filament emits only in the vicinity of the molecule of active material, we 
compute an a for the partly coated filaments which is much greater than 
the values (0.5 X 10** to 1.5 X 10^) given above for standard filament. 
The fact that the b obtained for filaments coated merely with a few widely 
separated molecules is the same as that obtained with a complete coating 
shows that the reduction of the work function at the metal surface can 
be brought about by a very small group of molecules. Under these condi- 
tions it seems reasonable to suppose that the only important effect of the 
molecule of active material is to lower the restraining voltage in its own 
vicinity and thus facilitate the passage of electrons from the metal core. 
The number of electrons that can avail themselves of such a molecular 
opening is limited to those presenting themselves with a sufficient out- 
ward velocity, and this in turn is determined by the properties of the core 
material. Since the core materials used have values of a greater than 
those which we find for the standard filaments it does not seem so strange 
that the values of a for the partly coated filaments should be found to run 
higher than those for completely covered filament. 

We hope that our present experiments will throw morejight on the 
factors involved in the escape of electrons through these minute activated 
areas. Our information is at present too meager to warrant an opinion 
as to whether an electron on its way out remains for some time as a 
part of the molecule of active material or merely slips past it. The 
number of electrons passing out through one molecular opening in a 
second may be of the order of ten thousand, and that this rate may 
persist for some time is indicated by the rather slow rate of decay of 
activity. This proves at least that no irreversible chemical change in the 
active coating is involved in the emission of an electron. Perhaps a more 



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{Jg-,"^] ELECTRON TUBES. 8 1 

Striking proof of this is found in certain of our filaments which through 
a life of twenty thousand hours have emitted fifteen times more mass of 
electrons than the mass of their coating. 

Another factor of considerable importance in connection with the use 
of Wehnelt oxides is the facility with which they emit electrons when 
bombarded by electrons or by positive carriers. The factors governing 
the emission of secondary electrons are not well understood even in the 
case of pure metals. Experiments which we have performed with re- 
distilled mercury surfaces indicate that the secondary emission may 
become very small when an absolutely clean siu^ace is obtained. With 
Wehnelt oxides the secondary emission may be comparatively large, 
several electrons being liberated by each one that strikes the surface. 
Under the bombardment of positive carriers, however, secondary electron 
emission does not appear to take place so readily, and our experiments 
have not as yet shown evidence of more than a few electrons emitted 
per impact. This negatives the idea, which a few people have held, 
that positive ion bombardment is a controlling factor in electron emission 
from oxide coated filaments. * 

In conclusion, it may be remarked that while oxide coated filaments, 
under the pressure of necessity, have been developed to the state where 
they can be manufactured and used on an immense commercial scale as 
evidenced by their employment in more than half a million vacuum tubes, 
and while they easily hold the field as the most economical, and longest 
lived, source of electrons available for electron tube devices, we have not 
as yet by any means reached the limit of their possible development. 
The physical constants delimiting the operation of pure metal filaments 
are well known for the metals now available, and there is no apparent 
avenue by which their efficiency can be materially increased. Marked 
advance can only be expected when we depart from pure metals by mixing 
or coating them with other materials. In the case of the oxides, which 
at present furnish the best material for coating, it is not at all unusual to 
find sporadic cases of enormously greater activity than the average whicl^ 
we obtain by commercial coating processes. The limit to which im- 
provement may be expected to extend can only be determined when 
the factors governing electron emission from the oxides are as well 
understood as are at present those governing electron emission from the 
pure metals. It is more than probable that in the process of obtaining 
this knowledge about the oxides we will find new light thrown upon the 
process of emission from pure metals as well. 

Rbsbarch Laboratories of American Telbphonb & Tblbgrapm 
Company and Western Electric Company, Inc. 



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82 H. D. ARNOLD. ^^SSSS, 

BiBUOGRAPHY FOR THE PHYSICS AND CHEMISTRY OF OXIDB CATHODES. 

1. Cooke, H. L. and Richardson, O. W. Absorption of heat produced by the emission of 

ions from hot bodies. II. Phil. Mag. (6), 26, 472, 1913. 

2. Deininger, F. Austritt negativer lonen aus einigen glOhenden Metallen und aus glQ- 

hendem Calciumozyd. Ann. d. Phys. (4). 25, 258, 1908. 

3. Fredenhagen, K. Ueber die Elektronenemission des Platins und (iber die Wirksamkeit 

der Oxydelektroden. Leipz. Ber., math.-phjrs. Kl., 65* 42, 1913. 
'4. Fredenhagen, K. Das Verhalten der Wehneltelektrode in verschiedenen Gasen. Phjrs. 

ZS., /5, 19, 1914. 
$. Gehrts, A. Die Ursache der Elektronenemission von Oxydkathoden. Verb. d.D.P.G.* 

/5, 1047. 1913. 

6. Germershausen, W. Die Elektronenemission der CaO-Elektrode im Vakuum. Phjrs. 

ZS. 16, 104, 19x5. Ann. d. Phys., 5^. 

7. Horton, F. Discharge of negative electricity from hot calcium and from lime. Phil. 

Trans., A207, 149. 1907; also Proc. Roy. Soc., A70, 96, 1917. 

8. Horton. F. Ionization produced by certain substances when heated on a Nemst filament. 

Camb. Phil. Soc. Proc., 27, 414, 1914. 

9. Horton, F. On the action of a Wehnelt cathode. Phil. Mag. (6), 28, 24, 1914. 

ID. Horton, F. Origin of the electron emission from glowing solids. Phil. Trans. A214, 

277. 1914. 

11. Jentzsch, F. Ueber die Elektronenemission von gltthenden Metallozyden. Ann. d. 

Phys., 27, 129, 1908. 

12. Richardson, O. W. Die Absabe negativer Elektrizitat von heissen Korpem. Jahrb. d. 

Rad. and El. /, 300, 1904. (Synopsis). 

13. Richardson, O. W. The kinetic energy of the ions emitted by hot bodies. II. Phil. 

Mag. (6), 18, 681, 1909. 

14. Richardson, O. W. The ions from hot salts. Phil. Mag. (6), 26^ 452, 1913. 

15. Schneider, H. Die Energie der aus gltthenden CaP entweichen den Elektronen. Ann. 

d. Phys., J7. 569, 1912- 

16. Schottky, W. Bericht ttber thermische Elektronenemission. Jahrb. d. Rad. and £1., 

72, 149, 191 5. (S)mopsis.) 

17. Wehnelt, A. Ueber den Austritt negativer lonen aus gltthenden Metallverbindungen 

und damit zusammenh&ngende Erscheinungen. Ann. d. Phys. (4), 14* 425, 1904. 

18. Wehnelt, A. On the discharge of negative ions by glowing metallic oxides, and allied 

phenomena. Phil. Mag., /o, 80. 1905. 

19. Wehnelt, A. and Jentzsch, F. Ueber die bei der Elektronenemission gltthender Korper 

auftretenden Temperaturanderungen. Verh. d. D. P. G., 10, 605, 1908. 

20. Wehnelt, A. and Jentzsch, F. Ueber die Energie der Elektronenemission. Ann. d. 

Phys., 28, 537. 1919- 

21. Wehnelt, A. and Liebreich, E. Energie der Elektronenemission gltthender Korper. 

Phys. ZS., 75, 548, 1914- 
p2. Willows, R. S. and Picton. T. Notes on the behaviour of incandescent lime kathodes. 
Proc. Phys. Soc. London, rj, 257, 191 1. 
3. Wilson, W. The loss in energy of Wehnelt cathodes by electron emission. Proc. Nat. 
Acad. Sci. j. 426, 191 7. 



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NoTi?^^'] DETERMINATION OF GAS VISCOSITY. 83 



NOTE ON THE END CORRECTION IN THE DETER- 
MINATION OF GAS VISCOSITY BY THE 
CAPILLARY TUBE METHOD. 

By Willard J. Fishbr. 

Synopsis. 

Assumptions Underlying Fisher's Formula for the End Correction, — ^Experiments 
by Benton having pointed to the conclusion that Brillouin's formula for the end 
correction represents the facts fairly well, whereas Fisher's does not hold even 
approximately; the writer points out that the experimental conditions assumed in 
the two formulas are essentially different. The use by Benton of comparatively short 
tubes with square cut ends gives a turbulent condition at the ends similar to that 
assumed by Brillouin. whereas Fisher assumes a slow stream-line flow such as 
could be attained only by the use of long tubes with gently tapered ends. The * 
conclusions reached by Benton are therefore to have been expected. 

TN reply tp the note by A. F. Benton (Phys. Rev., 14, p. 463, 1919) 
^ "On the End Correction in the Determination of Gas Viscosity by 
the Capillary Tube Method," it may be said that the approximate 
formula for kinetic pressure drop proposed by me (Phys. Rev., 32, p. 
216, 1911) is based on the following suppositions: 

1. Such a low speed in the tube that the stream lines within are all 
parallel to the axis and expansion of the gas does not result in change in 
temperature, the necessary heat being supplied by conduction through 
the tube walls; 

2. Both ends of the bore so gently tapered that the gas stream flows 
without anywhere leaving the glass; so that from stationary gas in the 
high pressure reservoir to stationary gas in the low pressure reservoir 
there is continuous stream line flow without turbulence. 

Unfortunately neither of these conditions W2is explicitly stated in my 
note, though both clearly underlie the use made of Boyle's law and 
Bernoulli's theorem. I regret that my obscurity in . expression should 
have led Mr. Benton to apply a correction formula in an experimental 
case to which its theory is entirely inapplicable; for the emergent jet 
from a square ended tube of diameter not small in proportion to its length 
is surely an illustration of stream line flow, and expansion within such 
a tube is known from published experimental data to be anything but 
isothermal ; there is a decided temperature fall along such a tube, very 
pronounced as the exit is approached. 



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84 WILLARD J. FISHER. [&!ra^ 

The correction formula of Brillouin is deduced for a tube cut off square 
at each end, and so for a turbulent squirt at the exit; also, the gas is 
assumed to flow as a liquid, without expansion within the tube, so that 
the kinetic energy wasted in turbulence and without pressure drop at the 
exit is entirely derived from pressure drop at the inlet. No account is 
made of the vena contracta. 

It is interesting to note that Brillouin's correction, as applied by Mr. 

Benton, gives results which represent his experimental data much better 

than the correction based on stream line exit; and also that it gives for 

mass delivered amounts uniformly higher than experiment, and higher 

by amounts not to be attributed to errors of observation. This is to 

be expected as a consequence of reactions during ^expansion within the 

tube, and not only of vena contracta effects. 

Department of Physics. 

The University of the Philippines, 
Manila. P. I.. 

February 13. 1920. 



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Second Series Augtist, iq20 Vol. XVI., No. 2 



THE 

PHYSICAL REVIEW. 



THE EXISTENCE OF HOMOGENEOUS GROUPS OF 
LARGE IONS. 

By Oswald Blackwood. • 

Synopsis. 

Nonexistence of groups. — Certain observers have found evidence indicating 
that the large ions produced by spraying water constitute several distinct groups 
each having a definite mobility. Using an apparatus similar to theirs, the author 
fails to confirm this result but finds that the ions distribute themselves continuously 
over a wide range with all intermediate mobilities present. In other words, he 
finds a continuous spectrum of mobilities and not a band spectrum. Conclusive 
proof of this has been obtained by a series of mobility determinations made with a 
Zeleney tube having a "resolving power" twenty times as large as that of the 
apparatus mentioned above. 

Age and mean mobility. — The mean mobility of the ions decreases with time 
after formation at a rate indicating that the rate of condensation of water vapor 
on any ion is constant and independent of its size. 

Growth of ions dependent upon the humidity of the air. — Having replaced the 
water sprayer by a red-hot platinum wire as a source of ionization, it was possible 
to control the water vapor density. Drying the air causes a decrease in the rate of 
growth of the ions. 

Growth of ions probably due to condensation of water vapor* — The experimental 
facts are explained by assuming that large ions grow by condensation ol water 
vapor on a nucleus. This assumption is consistent with the views as to the nature 
of the large ion held by Barus, Aitken, Thompson, and others. 

NOLAN and McLelland^ in 1916 and Nolan* in 191 7 published papers 
presenting evidence which indicates that the spraying of distilled 
water orthe bubbling of air through mercury produces large ions having 
a wide range of mobilities. The most mobile ion has a mobility much 
greater than that of the small ion produced in air by X-rays, while the 
most sluggish one approximates that of the stable Langevin ion found 
in the atmosphere. Moreover, the mobilities do not distribute them- 
selves continuously over this range but constitute several distinct groups 

* Proc. Roy. Irish Acad., Vol. 33, p. 9, p. 24, 1916. 
« Proc. Roy. Soc., A, Vol. 94. 191 7. 

85 



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86 



OSWALD BLACKWOOD. 



rSSCOND 



with intervening gaps. In other words, there seem to be band spectra 
of mobilities and not continuous spectra. 

Recently the investigation has been extended, and similar indications 
have been found with regard to the ions produced by bubbling air 
through alcohol^ or by passing it over phosphorus.* 









Table I. 








Mttcory. 


Alcohol, 




Water 

(Sjwy), 


Ions Newly Produced. 


Long Time IntervmL 


Phosphorui, 
G, 


A, 


nndriek Air. 


Dried. 


Undried Air. 


E. 


6.51 














3.27 














1.56 




• 










1.09 










1.10? 




.53 










.50 




.24 










.22 


.22 


.12 










.12 


.092 


.046 




.024 


.043 


.043 


.049 


.053 
.028 


.013 


.014 




.02 




.017 


.018 






.0068 




.0064 


.0077 


.0074 


.0043 


.0040 




.0045 


. 


.0040 


.0041 






.0021 




.0022 


.0023 


.0024 


.0010 


.0013 


.00 
.00056 


.0013 




.0014 
.00063 


.0012 
.00064 


.00038 


.00034 








.00034 
.00015 


.00031 
.00015 
.000085 
.000053 



Table I. gives a list of the mobilities of the groups produced by each 
method. In column A it will be noticed that the first two groups have 
mobilities greater than those of the small ions produced in air by X-rays. 
Column G gives a list of mobilities of the groups produced by passing 
air over phosphorus. This list is highly significant because the range of 
mobilities is large, and because the fourteen mobility values constitute 
an approximate geometric progression. 

In view of the fact that no plausible hypothesis has been suggested to 
account for the production of several classes of ions of which the mobili- 
ties form a geometric progression, the groups have seemed especially 
worthy of investigation. In order to test out the apparatus before 
attempting to discover whether the groups exist in the ionization pro- 

1 Proc. Roy. Irish Acad., A, Vol. 34, p. 57, 1918. 
* Ibid., A, Vol. 35, p. I, 1919. 



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Vou XVLI 
No a. J 



HOMOGENEOUS CROUPS OF LARGE IONS. 



87 



duced by other methods; Nolan's work on the mobilities of the ions 
produced by spraying distilled water was repeated with slight modi- 
fications of apparatus to be described later. The author, to his surprise, 
failed to confirm the existence of the groups. 

The apparatus first used was essentially that of McLelland and Nolan 
and is shown in Fig. i. The parts requiring especial notice are: 

1. The air pressure regulator, A, 

2. The sprayer, C. 

3. The capillary C 

4. The ion testing tube F, 

1. .The air pressure regulator -4 is a vertical tube partly submerged 
in water. The bubbling of air escaping from the lower end of this tube 
keeps the pressure approximately equal to the water pressure at that end, 

2. The sprayer C was made entirely of glass and was especially designed 
for this investigation. With an excess air pressure of one half atmos- 
phere — the value used in all the measurements — a dense fog of spray is 
produced and the quantity of air required is only 30 c.c. per second. 




E-^l^f^l iHM 



Fig. 1. 

3. The capillary tube C may be replaced by others of different bores, 
thus varying the velocity of the air current at will, while keeping the 
air pressure constant. 

4. The ion testing tube F consists of a brass cylinder 160 cm. long and 
5 cm. internal diameter, fitted with a co-axial cylindrical brass electrode 
140 cm. long and 2 cm. in diameter. This electrode is supported by 
sulphur plugs mounted in grounded guard-rings. The electrode is 
connected to a pair of quadrants of a Dolezalek electrometer having a 
sensitiveness of 70 cm. /volt with the scale at a distance of 200 cm. 
The outer cylinder may be connected to any portion of a battery of 100 
fresh dry-cells. 

On occasion, the rate of flow of air through the apparatus may be 
measured by attaching the tube of a gasometer at G. 



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88 OSWALD BLACKWOOD. f^SSI? 



LSbkim. 



Method of Experiment. 



Air from the laboratory system is filtered by passing it through a tube 
packed with glass wool. At -B, Fig. i, the stream is divided, part going 
through the sprayer C and part through the capillary C. Reunited 
at D, the air enters the ion testing tube F. 

The ion testing tube of the type described was designed by McLelland 
and has been used extensively in the determination of mobilities of large 
ions. These ions are carried forward in the tube by the air current 
and are simultaneously deflected toward the central electrode by the 
electric field. If the intensity of the electric field be gradually increased, 
the ion current to the electrode increases until the field becomes irttense 
enough to drive all the ions to the electrode, beyond which point the 
current is saturated. It can be shown that — neglecting the effects of 
diffusion, recombination and distortion of the fields by electrode supports 
and by the presence of the ions — if ions of only one mobility are present 
the current-voltage curve is a straight line through the origin, breaking 
sharply at the critical voltage and becoming parallel to the voltage axis. 
If, however, ions of several mobilities are present, the resultant curve 
shows several breaks in slope, each corresponding to a certain mobility. 
(See Fig. 5.) 

It can be shown that the critical voltage V for ions of mobility K is 
given by the equation^ 

a and b being the radii of the electrode and the cylinder, respectively, 
Q the quantity of air traversing a cross-section of the tube each second, 
and L the length of the electrode. 

Sources of Error. 

In the early observations much error was caused by the falling voltage 
of the accumulators. The charge induced on the central electrode by a 
decrease of only 1/5 volt, in a total of 160 on the outer cylinder, caused 
an electrometer deflection of several centimeters. This variation became 
negligible when the accumulators were replaced by dry cells. 

A persistent error was due to the variations of the sprayer. Consecu- 
tive readings usually agreed within two per cent., but the positions of 

log* b/G 

» This formula becomes exact for a cylinder of finite length if the part ; — be 

2rX< 

replaced by the measured capacity of the portion of the insulated system which is exposed 

to the air current. See W. F. G. Swann, "The Theory of Electrical Dispersion into the 

Free Atmosphere." Terrestrial Magnetism and Electricity, Vol. 19. PP. 81-88, 1914. 



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V0L.^XVI.J HOMOGENEOUS GROUPS OF LARGE IONS. 89 

the breaks in slope of the current voltage curves shifted to such an 
extent in successive curves that it was usually impossible to determine 
mean curves showing breaks. (See Fig. 2.) In the effort to eliminate 



Fig. 2. 

this shifting, three different types of medicinal sprayers were tried before 
the glass one already described was constructed. 

Results. 

In certain cases the current-voltage curves are quite smooth. (See 

Fig- 3-) In others breaks in slope are present which are quite as definite 

as those exhibited by Nolan. (See Fig. 5.) His value for the ratio of 

successive mobilities, however, is not found in a single instance. This 



Fig. 3. 

ratio, in the present investigation, is usually about 2.0 and is never as 
high as 3.4, the mean value determined by him. 



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90 



OSWALD BLACKWOOD, 



rsscoKD 
LSiims. 



Being^ convinced that the mobility values did not fit into the group 
system of Nolan, an attempt was made to ascertain whether my values 
determined from day to day fitted into any group system. Fifty-nine 
breaks were worked over in detail using various values of the air velocity 
and, in certain instances, introducing metal tubes between the sprayer 
and the testing cylinder in order to increase the time intervening between 
the production of the ions and their arrival at the testing tube. Table II. 
shows the mobility values. For convenience they have been arranged in 
classes, but if they are represented graphically by points along a straight 
line no tendency to form groups is to be observed. 

Table II. 

Mobility Vabues Determined by the Author. 



Time After 
Production. 


MobiUtes of Ions. 


60 sec. 




.0016 


.0027 


.0036 


.0080 . 


.016 


.028 










.0037 


.0070 


.017 


.037 


100 " 


.0006 


.0013 
.0017 




.0042 
.0035 
.0043 


.0082 


.012 
.013 
.014 




600 " 


.0003 


.0010 


.0020 


.0043 


.0080 








.0006 


.0011 


.0022 
.0027 


.0045 








1200 " 


.00055 


.0011 


.0016 


.0045 


.0070 


.015 






.00046 


.0012 


.0014 


.0039 


.0060 








.00077 


.0010 


.0017 


.0030 


.0065 








.00080 


.0010 


.0021 
.0020 
.0026 


.0037 
.0036 
.0042 
.0053 


.0060 







If then we disregard breaks, the smooth curve may indicate either a 
continuous distribution of mobilities or it may indicate that the sharp- 
ness of the break in the theoretical curve for a single class of ions has 
been obscured owing to the failure to obtain the ideal conditions of the 
theoretical method. 

Criticism of Method. 

The McLelland ion tube is well suited for the measurement of mobili- 
ties which are widely separated, but if the number of breaks is large the 
distance between breaks is small and, owing to experimental errors, a 
smooth curve results. In the investigations carried on by McLelland 
and Nolan, in most instances not more than six breaks were located for 



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Vol. XVI.I 
No. a. J 



HOMOGENEOUS GROUPS OF LARGE IONS. 



91 



any individual current- voltage curve. It will be of interest to see how 
little such a curve differs from a smooth one corresponding to a con- 
tinuous distribution of mobilities. Fig. 4 is a theoretical curve showing 
breaks corresponding to six different classes of ions all present in equal 
concentrations. The ratio of each mobility to the one preceding it is 
1.9 which is the approximate value found by McLelland and Nolan for 
the ions produced by passing air over phosphorus. It will be noticed 

McLelfahct Tub^ Curye, . 




Fig. 4. 

Theoretrical Curve Indicating Existence oi Groups. 

Fig. 5. 

Experimental Curve Determined by Nolan. 

that the breaks, especially (a), (6), and {c) are so slight that they would 
easily be masked by experimental errors. 

Nolan himself admits the possibility of a smooth curve being drawn 
through his points. Regarding the only curve showing several breaks 
which he exhibits (see Fig. 5), he writes: 

'*It might be said that a smooth curve might be drawn with almost 
equal exactness, showing that, instead of an abrupt step in mobilities, 
there was a gradual shading off from one to another, with ions of all 
intermediate mobilities present. With the object of eliminating this 
sort of uncertainty, and of obtaining as accurate values as possible for 
the mobilities of the different ions, the current-voltage curve was worked 
over in detail many times, each section being investigated under con- 
ditions specially chosen to bring out its features."^ 

It is on the evidence of such breaks as these that Nolan in his earlier 
paper, based the claims for the existence of positive and negative ions 

iProc. Rdy. Irish Acad., A, Vol. 33, P. 12, 1916. 



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92 OSWALD BLACKWOOD. [ISSS 

whose mobilities are higher than any previously discovered for normal 
ions generated by X-rays, ultra-violet light, etc. To the writer's knowl- 
edge such abnormally high mobilities for positive ions have never been 
found by other observers though methods of much higher sensitiveness 
have been used, and though the experiments have been carried out not 
only in the prsence of water vapor but also in carefully dried air in which 
the mobilities are distinctly higher. It is indeed true that abnormal 
mobilities have been found in the case of negative ions at low pressures 
for common gases, and even at atmospheric pressures for monatomic 
gases. These high mobilities, however, are believed to be due to the 
presence of free electrons. 

In a more recent investigation* having modified his apparatus by 
replacing the cylindrical ion tube by a plate condenser, and by intro- 
ducing the nozzle of the sprayer directly into the field between the plates, 
Nolan obtains discontinuities in "his curves of an entirely different order 
of magnitude from those which occur in the earlier experiments. These 
discontinuities are certainly of a real nature and it is not in questioning 
their existence that one can attempt to correlate the present results 
with those of Nolan. It must, however, be pointed out that the breaks 
in his current-voltage curves may be produced as well through discon- 
tinuous changes in the electric fields driving the ions to the electrode 
as by a discontinuous distribution of mobilities of the ions themselves. 
The possibility of such an explanation of the curves of Nolan seems 
worthy of discussion. He himself admits regarding the observational 
values of his field strengths, that the applied voltage differs from that 
corresponding to the effective values of the fields by from zero to 4.5 
volts. It is noticeable, also, that the discontinuities in the ion currents 
are comparable in magnitude to possible sudden changes in potential of 
the same order of magnitude as the values of the uncertainties in the 
potential difference which Nolan admits. Exactly how these discon- 
tinuities might occur, one cannot decide. It is possible that in increasing 
the negative value of the field strength, different sizes and different posi- 
tively charged droplets produced by spraying, are successively removed 
from the space between the electrodes, thus discontinuously changing the 
values of the field. Nolan himself states that the uncertainty in his 
fields can be explained on the assumption of the disappearance of small 
positively charged droplets from between the plates. It is also to be 
noted that he obtains values of the positive and negative mobilities which 
are many times as great as the values obtained in dry air by the classical 
methods. It seems possible that the explanation of these mobilities 

»Proc. Roy. Soc.. A, Vol. 94, 1917. 



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N^a?^^'*] HOMOGENEOUS CROUPS OP LARGE IONS, 93 

lies in the fact that the absolute values of his fields are not definitely 
known. For example, for a negative carrier whose mobility he gives as 
188 cm. /volt X volt/cm. he finds that the break in his curve occurs at 
+3.5 volts. When the potential of the lower plate is further increased 
to +3.75 volts, no negative ions from the sprayer reach the upper elec- 
trode and the electrometer current becomes zero. Nolan assumes, 
therefore, that at +3.75 volts the field driving the negative ions toward 
the upper electrode is zero. What the experiment shows, however, is 
not that the field is zero, but that it is not strong enough to drive the 
ions to the upper electrode before they are carried past the electrode by 
the air current. The ions are probably driven toward the upper plate 
even though they do not actually reach it. For his experimental arrange- 
ment he finds Vk = QA/LB « 47 (in which A, L^B, are the dimensions 
of the plate condenser, Q is the quantity of air traversing it each second, 
k the ionic mobility, and V the potential difference between the plates). 
Having assumed that the critical voltage (+3.75 — 3.50) = + 0.25 is 
necessary to drive the ions across the distance between the plates in the 
time during which they travel the length of the condenser, he interprets 
the mobility * as being equal to * = 47/(375 — 3.50) = 188. If one 
assumes under these conditions that he was actually measuring the 
mobility of the normal negative ion, which is 1.8, the same initial break 
in the curve could have been caused if the actual value of the field were 
47/1.8 = 26. This field strength could possibly have been caused by 
the electrification of the air produced by the sprayer which, as has been 
stated, is introduced directly between the plates of the condenser. As 
in his paper no mention is made of an attempt to verify the values of 
the fields by exploring electrodes or otherwise, there seems to be no apriori 
reason why one interpretation of this result is not just as adequate as the 
other. Too much confidence, then, cannot be placed on the interesting 
results of Nolan until there is more certainty as to the values of his fields. 

The Zeleney Method. 

It was obvious that, using the method of McLelland and Nolan no 
positive decision as to the real existence of the groups of ions could be 
obtained. Recourse was accordingly had to a modification of the Zeleney 
method which seems much better adapted for giving a decisive verdict. 

The electrode of the ion tube already described was cut into two 
sections L' and L", 105 and 35 cm. long respectively, which were separ- 
ated by a small air gap. The electrode L' was grounded and L" was 
connected to the electrometer. (See Fig. 6.) 



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94 oswald blackwood. 

Theory. 

The ions, produced in the same manner as that described in the previ- 
ous section, are carried by the stream in a direction parallel to the axis 
of the tube. Disregarding diffusion, if there is no potential difference 
between the outer and inner cylinders, none of the ions will reach the 
inner electrodes. If, now, the outer cylinder be raised to a potential 






^^^^^^^^^EMS^^^WM^m 







r 



|i|t|i|<l ^|l|l|'l•l 



Fig. 6. 



above the inner ones, all the positive ions entering the tube within a 
distance r of the axis are driven to the electrodes, while all others escape. 
As the potential difference increases, the value of r also increases and, 
consequently, with it the ion current to the electrodes. At a critical 
voltage V, r becomes equal to the radius of the cylinder and all the ions 
are driven to the electrodes so that the current reaches its maximum. 
As the potential difference is still further increased, more and more ions 
are driven to the first, grounded, electrode, and consequently the electro- 
meter current from L" diminishes until, at a second critical voltage F", 
it becomes zero. 

Neglecting the influence of recombination and diffusion of the ions, 
and assuming that the electric field is radial at all points in the tube, it 
has been shown that the Zeleney tube gives a current-voltage curve of 
the form shown in Fig. 7 {€)> The nature of this curve may be deduced 
from the curves A and B (Fig. 7) which are determined when the electro- 
meter is connected (as in the McLelland arrangement already described) 
(a) to^ the first electrode V and (6) to both electrodes. The curve (C) 
of which the ordinates are evaluated by subtracting the corresponding 
ordinates of A from those of -B, therefore represents the ion current to L" 
when V is grounded. 

* Bloch. Ann. de Chemie et de Physique (8), Vol. IV, p. 25. 1905. 



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VoL.XVI.1 
No. a. J 



HOMOGENEOUS CROUPS OF LARGE IONS. 



95 



From the curves A and -B it is evident that V is the voltage causing 
saturation when the electrode has the length (U + L") while V" causes 
saturation using an electrode of length V. 

For ions of mobility ft, we have in the two cases: 

Ze'lenei^ Tub€> Curye\ 




k = 



Qlog^b/a Qlogcb/a 



YL = ^' 



(I) 



(2) 



(L' + L") • 

The saturation voltage V being given for ions' of mobility k, it may be 
computed for ions of mobility K' from 



k/K' -^ 



v ■ 



(3) 



If the maximum ion current be known, the current-voltage curve for 
the Zeleney apparatus may be constructed for ions of a given mobility 
with the aid of equations (i), (2), and (3). 

Figure 8 (-4), (B), (C) shows the forms and relative positions of the 
current voltage curves of the Zeleney apparatus for ions of mobilities 
•O043, .0010 and .0004. These are three mobility values for successive 
groups as found by Nolan for ions from spray. The dotted line shows 
the summation curve determined if the ions of the three groups are 
present in equal concentration. 

If the number of groups should increase, and the interval between 
successive groups consequently become smaller, the broken line would 
be less deeply notched and, if the ions did not constitute distinct groups 
but distributed themselves continuously over the range from .0043 to 



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96 OSWALD BLACKWOOD, 

.0004, the curve would be smooth as indicated by the dotted line in Fig. 9 A . 
To decide whether the groups exist or not, it is therefore sufficient to 
decide whether the experimental current-voltage curve has one or more 
than one maxima. 

Similarly, Fig. 9 B shows the theoretical curve given by the McLelland 
tube if the same three groups of ions are present in equal concentration. 
The dotted line shows a smooth curve such as might be given by a 



Fig. 9. 

continuous distribution of mobilities. Comparing the curves A and B 
it is evident at a glance that the Zeleney apparatus affords a more 
decisive test as to the existence of the groups. 

We shall arbitrarily define the ** resolving power " of each instru- 
ment for any type of ions as the ratio bd'jcc' (Fig. 9 (-4) and (5)). In 
the case of the three breaks in each curve, the *' resolving powers " 
are approximately. 



Group. d. 


a. 


d*'. 


Mean. 


'« Racoi^n^ Ponrar. " i Zelcncy Tube 1 2. 

Resolving Powers [ McLelland Tube ' 0.1 


1. 
0.07 


\ 
0.025 


1.2 
0.065 



The resolving power of the Zeleney tube for the curves shown is accordingly 
about 18 times as great as that of the McLelland arrangement. 

Measurements with Zeleney Tube. 

Owing to the fact that the available time was limited, it was possible 
to determine only seven curves for spray ions using the Zeleney apparatus. 
In certain instances metal tubes were introduced between the sprayer 
and the ion tube in order to '' age " the ions or increase the time in- 
terval between their production and arrival at the testing tube. Two 
specimen curves for different ages are shown in Fig. 10. Several inter- 
esting conclusions may be drawn from their forms and relative positions. 



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VoL.XVI.1 
N<Ka. J 



HOMOGENEOUS GROUPS OF LARGE IONS. 



97 



Non-existence of Groups. 
The fact that this apparatus, having a " resolving power " many 
times greater than that of the McLelland arrangement, gives curves 
showing no discontinuities, seems conclusive evidence that a series 
of well-defined groups does not exist. E^ch curve shows one maximum 
and inversion point which indicates a preponderance of ions whose 




Fig. 10. 

mobilities lie on a narrow range. The curves also show, by the fact 
that they approach the voltage axis asymptotically, that other ions 
of very low mobility are also present. 

Effect of Ageing. 

When tubes are interposed between the sprayer and testing tube to 
" age " the ions, the center of gravity of the curve shifts to the right, 
indicating that the mean mobility has decreased. This agrees with the 
observations of Nolan. He explains this decrease as due to the dis- 
appearance of the smaller ions owing to their diffusion to the walls of 
the containing vessel; to their recombination to form larger neuclei; or 
to their growth by condensation of water vapor. 

A more striking series of curves was obtained when the sprayer was 
replaced by a red-hot platinum filament as a source of ionization. This 
wire was found to afford a copious supply of positive ions, but a negligibly 
small number of negatives. 

In this case, as before, tubes were interpx)sed between the sprayer and 
the ion testing cylinder in order to age the ions. Several curves for 
different ages are shown in Fig. ii. In view of the fact that a pre- 
ponderance of the ions for any age have mobilities lying on a narrow 
range on either side of the mobility value for the ion which is present 
in greatest numbers, an effort was made to interrelate the ages with 



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98 



OSWALD BLACKWOOD. 



[ 



Sbcoms 



the respective mobility values for the maximum-concentration ion. 
The critical voltage corresponding to the maximum ion current was 
therefore determined for each curve, and the mobility values were com- 
puted with the aid of equation (i). The results are shown in Table III. 
If one plots the logarithms of the values of these mobilities as ordinates 



Fig. 11. 



Table III. 

Mobility Values for Ions Present in Greatest Concentration. 





A«e. 




3. 


4- 


6. 


8. 


13. 


i6. 


33. 1 33. 


45. 


58. 


70. 


Mobility. . 


0.06 


0.042 


0.029 


0.026 


0.023 


0.020 


0.016 


0.012 


0.009 


0.0075 


0.0065 


Log age . . 


0.30 


0.60 


0.78 


0.90 


1.08 


1.24 


1.351 


1.51 


1.65 


1.76 


1.85 


Log (*X 
1.000).. 


1.78 


1.62 


1.46 


1.41 


1.36 


1.30 


1.20 


1.08 


0.96 


0.87 


0.81 



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nJ-2?^^^'] homogeneous groups op large ions. 99 

against the logarithms of the corresponding ages as abscissas, the points 
are found to lie sensibly along a straight line of which the slope is 6/10 
(see Fig. 12). This differs from 2/3 by 10 per cent. If we assume 
2/3 to be the correct value, we may interrelate the age of the ions with 
the mobility of the maximum-concentration ion as follows: 

3/2 log fe + log / = log C, 

(4) 

in which k represents the mobility of the maximum-concentration ion, 
/ the age of the mixture of ions (defined on page 12), and C is an empirical 
constant. If in accordance with the ** hard elastic sphere " theory 
of J. J. Thompson^ we assume that the mobility of a large ion varies 
inversely with its radius squared, equation (4) may be written: 



4/3^r 
or 

/ = C/C'v; 
.'. dv/dt = C7C, 



Fig. 12. 

C being a constant of proportionality, and v the ionic volume. This 
indicates that the ions are growing at a constant rate, independent of 
the radius. 

' Thompson, Conduction of Electricity through Gases. 



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loo oswald blackwood, (isss? 

Humidity and Rate of Growth of the Ions. 

Using the hot-wire method of ion production, it was possible to con- 
trol the water vapor density in the air which was driven through the ion 
tube. The air was dried by passing it over CaCU and PjOb. The air 
was then charged with water vapor by bubbling it through a column 
of water, the temperature of which was raised in successive ** runs," 
so as to increase the vapor density. It was found that for a given age 
increasing the vapor density decreased the mean mobility of the ions, 
which indicates that the presence of water vapor is favorable to the 
growth of the ions. 

The conception which one gains from the above experiments as to 
the nature of the formation of the large ions is consistent with the views 
published in the papers of Barus,* Aitken,* Pollock,' Lenard,* and others. 
It is not at all inconsistent with the experiments of C. T. R. Wilson as 
explained by Thompson.' According to our results, the original nucleus 
of the large ion may be an agglomeration of a few molecules of water or a 
few particles of dust which have gathered a charge either in the process 
of formation (spraying of water), or by picking up a charge while passing 
through the ionized gas surrounding the hot platinum filament. These 
nuclei, due in part to their charge, may continue to grow by condensation 
of water vapor or by agglomerating into larger units, at a rate depending 
on the concentration of water vapor and on the time interval in which 
the ions have had a chance to reach equilibrium. The detection of the 
particle or nucleus as an ion, and possibly to some extent, its dimensions, 
are dependent on its acquiring a charge at some stage of the process. 
The explanation of these results in no way demands the growth of the 
large ion through the clustering of water molecules around a single charge. 

Summary. 

I. Using the McLelland method for the determination of mobilities 
of large ions, it is shown by a series of experimental curves that we are 
not justified in concluding that a series of groups of ions of definite 
mobility exist. 

II. It is also shown that the breaks in the curves obtained by the 
author which indicate the existence of groups of definite mobility, are 
too uncertain to permit of their interpretation in this way in view of the 
possible magnitude of experimental errors. 

III. It is also pointed out that the experimental curves obtained by 

» Amef. Jour. Science. 33. p. 107, 1912. 

> Aitken, Roy. Soc. Edinburgh Proc., 37. p. 215, 1916-17. 

» Pollock, Phil. Mag., Vol. 29, p. 514, 191 5. 

* Lenard. Ann. Physik, Vol. 47, 44. July, 191 5. 



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No!"a?^^'*] HOMOGENEOUS GROUPS OF LARGE IONS, lOI 

Nolan in a more recent paper in which the breaks are unquestionably 
present, may be interpreted in other ways not involving the assumption 
of the existence of groups of ions of abnormally high mobilities. 

IV. The problem was also attacked using the Zeleney method of 
mobility measurement which gives a much higher ** resolving power," 
than the McLelland method, with the result that no evidence was found 
for the existence of groups of ions of several different mobilities. 

V. Further results are given showing a relation between the mean 
mobility of the ions present and the time which has elapsed between 
the formation of the ions and the measurement of their mobility, in the 
case of ions formed by spraying water and from hot wires. These results 
indicate that the mobility varies as the 2/3 power of the reciprocal of the 
age, from which it is deduced that the rate of growth of the ions is 
constant. 

In conclusion I wish to express my gratitude to Dr. Millikan under 

whose direction this investigation has been carried out, to Dr. A. J. 

Dempster for occasional assistance, and to Dr. Leonard Loeb for aid in 

the interpretation of results and the revision of my manuscript. 

Rybrson Physical Laboratory. 
January 5. 1920. 



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I02 JOHN ZELENY. [^SS? 



ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. 

By John Zblbny. 

Synopsis. 

Surface Action in EUcirical Discharges from Points. — The lag phenomena shown 
by the discharges from some points indicate a special surface action. Various 
possible surface actions are discussed and attention is centered upon an adhering 
layer of gas molecules. Further evidence is sought in discharges from points 
made of different materials. 

Electrical Discharges from Water Points. Surface Electric Intensities and Slopping 
Voltages. — Discharges from water points begin impulsively. The surface intensity 
during positive discharges is independent of the current and a simple relation exists 
between values of this intensity, point radii and air pressures. Empirical relations 
are given connecting point radii and stopping voltages. The results are compared 
with those from similar metal points. 

Electric Fields for Water Points in Air, Oxygen, Hydrogen and Carbonic Acid, — 
A table of these fields is given for two water points with different gas pressures 
ranging from lo cm. to 87 cm. of mercury but no relation between these values and 
other constants was found. 

Comparison of Electric Fields for Points of Water, Glycerine and Methyl Alcohol, 
and of Stopping Voltages for These Liquids and for a Brass Point. — The comparison 
was made in air at different pressures, and no differences between the different 
substances were observed with the exception that some of the results for methyl 
alcohol were smaller than those for the other substances. 

Starling Voltages for a Brass Point Coated with Various Salts. — The surfaces were 
far from smooth but the positive discharge started at nearly the same potential 
from all of the different coatings, while the negative starting potentials varied 
greatly among themselves. 

Dependence of Critical Fields upon the Curvature of Surfaces of Points. — ^An 
explanation is given of the fact that the critical field required for the production 
of a discharge is larger the smaller the radius of the point. The dependence of 
the field at the surface of a point during a discharge upon the divergence of the 
field is shown experimentally. 

Discharge Currents for Points Made of Different Materials. — Testing for a possible 
ejection of ions from a surface by impact, similar points of platinum, brass, copper 
and water under the same conditions gave the same currents except that the negative 
current from water was slightly smaller than from the other substances. 

Possible Surface Factors in Point Discharges. 
I . The theory of the flow of electrical currents from pointed conductors 
which is generally accepted assumes that the ions which carry the dis- 
charge current are produced solely by collision with molecules of the 
gas of the few ions normally created in the gas by radiations from radio- 
active substances. Many of the general characteristics of these dis- 



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NoTa!^^'] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. IO3 

charges may be explained qualitatively on this theory by the known 
properties of ions, without the need of assuming any action at the dis- 
charging surface such as ejection from it of ions by the impact of those 
colliding with it or such as would arise if the ions met with difficulty in 
discharging to the metal surface. 

There are some features of these discharges, however, which indicate 
that at least under certain circumstances a special action does take place 
at the discharging surface.^ Thus for example the discharges from 
some metallic points begin very impulsively as the voltage applied is 
gradually increased, as if some resistance had been suddenly overcome; 
and what is even more significant, on decreasing the voltage after a 
discharge has started in these cases the current breaks off abruptly. 
An explanation of this sensitivity of some points, as such behavior is often 
called, must be sought in some condition at the discharging surface 
because points to all appearances similar differ very markedly in this 
property; and a point not possessing the property may be made to 
acquire it by treatment which does not appreciably change the form 
of the point. 

Edmunds* however ascribes the retardation in the commencement of 
discharges from points to the fact that the ions normally in the gas are 
few in number and that some time may elapse after a voltage is applied 
before ions may chance to assume a favorable distribution along that 
restricted region where the field is strongest and where accordingly 
ionization by collision can take place for the lowest permissible applied 
voltage. 

It is difficult to see why this argument should apply to some points 
and not to others to all appearances of the same form which do not 
show the lag phenomenon. Moreover, the abrupt stopping of a current 
which accompanies the lag in starting cannot be explained in this way. 

However, when a point is in a condition to show a lag in the com- 
mencement of a discharge, the discharge is often brought on by the 
sudden production within the field of force of an exceptionally large 
number of ions, a matter which will be considered more fully at a later 
time. 

2. What possible actions may we suppose taking place at a discharging 
surface' which surface conditions could aid or retard? We may suppose 
that electrons or ions are being pulled from the surface by the strong 
electric field; or that electrons or ions are being ejected from the surface 
by the impact of other ions against the surface; or that under some 

» See J. Zeleny. Phys. Rbv., N.S.. 3. p. 69. 1914. 
' P. J. Edmunds. Phil. Mag. (6), 28, p. 234. 19 14. 



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I04 JOHN ZELENY, I^SSl 

circumstances ions coming from the gas may find it difficult to discharge 
themselves to the surface. The state of the surface might influence 
greatly any of these actions. 

That the pulling of ions from the surface by the field plays any appre- 
ciable part in point discharges is made improbable by the results of 
Almy^ who working at distances of the order of a wave-length of light 
found that no discharge passed between the electrodes for fields as high 
as 1.7 X 10' volts per cm., although a discharge did pass with still higher 
fields. The field at the surface of a discharging point is ordinarily very 
much smaller than the field named and the only possibility of any such' 
action actually taking place lies in the fact that in Almy's experiments 
the conditions were not favorable for the multiplication by collision of 
any ions that might have come from the metal. 

The ejection of electrons from metal surfaces by the impact of ions is 
postulated in the explanation of some phenomena connected with dis- 
charges at low pressures , and a similar activity at the surface of a dis- 
charging point is not excluded. Ionization of gas molecules adhering to 
a metal surface by the impact of ions coming to it would produce effects 
similar to those resulting from ejection of electrons from the surface, 
and moreover might take place with either a positively or a negatively 
charged point. Neither of these effects however could change appre- 
ciably the voltage at which a current is observed to begin from a positively 
charged point, since a positive ion coming from the surface would be 
unable to ionize molecules of the gas by collision if the negative ion 
which produced it had not been able to do so, and without further increase 
these added ions could not give an observable current unless the highly 
improbable supposition were made that each original ion that strikes 
the surface gives rise to nearly a million new ions at the surface. The 
production of ions at the surface should result rather in an increased 
current for voltages above the critical one over the current due to the 
ionization produced by collision of those ions which originated in the 
body of the gas. See section 21. 

What seems to be the most probable part that the surface plays in 
the discharge phenomenon is that under certain conditions, owing to the 
presence of a non-conducting coating, ions from the gas find more or 
less difficulty in discharging themselves to the surface, and hence a 
larger voltage than usual is necessary for the commencement of the 
discharge. 

The lag in the commencement of the current from points can scarcely 
be laid to the accumulation of non-conducting dust on the surface, for 

i J. E. Almy, Phil. Mag. (6), i6. p. 456. 1908. 



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NoTaf^'] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. IO5 

Edmunds (loc. cit.) took great care to free the air from dust in the dis- 
charge vessel used; and points may be sensitive when no dust can be 
seen on the siuiace with a low power microscope. Small dust particles 
doubtless influence the magnitude of the current from a point to which 
they are adhering, but they would have to cover a large part of the surface 
to produce the large lag in starting, which is observed at times. 

The sensitivity in question cannot be due to contamination of the 
surface by volatile substances since it occurs with metal points which 
have been heated to incandescence.^ 

Gorton and Warburg (loc. cit.) have shown that with points made of 
copper or iron the sensitivity appears and disappears with the formation 
and reduction respectively of a layer of oxide. But sensitivity can 
scarcely be ascribed in general to the influence of non-conducting oxides, 
since it is known to occur with platinum points as well as with points 
made of other metals. 

A possible cause of the lag phenomenon applicable to all materials^ 
is to be found in the condensed layer, either of water molecules or of 
molecules of the surrounding gas, which is believed to cover the surfaces, 
of solid and liquid substances, for if this layer is a poor electrical con- 
ductor it is probable that under certain conditions it exerts a marked 
effect upon these discharges by preventing or retarding the passage of 
electricity from the gas to the metal point. 

That gaseous ions do not readily give up their charges to a metal 
surface is shown by the experiments of Gaede* who found that metal 
plates to which a discharge from a point had been allowed to flow ex- 
hibited a marked polarization when tested for the Volta effect. Gaede 
found that even 15 sees, after a measured quantity of electricity was 
allowed to flow from a point to such a plate, on immersing the plate irt 
an electrolyte, over one half of this charge could be recovered from the 
plate. It is natural to suppose that it is the non-conducting layer of 
condensed gas that keeps the ions from discharging readily to the metal. 

3. To account for the behavior of sensitive points by such a layer 
of gas or water molecules it is necessary to assume first, that this layer 
when solidly packed must be punctured and partially dissipated before 
a current of any considerable magnitude is able to flow to the surface, 
and second, that the layer is able to reform and thus interrupt the dis- 
charge when the current is below a certain value. 

On these assumptions sensitive points should be those having smooth 
homogeneous surfaces on which closely packed layers of Condensed gas 

> F. R. Gorton and E. Warburg, Ann. d. Phys., (4) 18, p. 128, 1905. 
* W. Gaede, Annalen der Physik (4), 14, p. 669, 1904. 



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I06 JOHN ZELENY, ^SSSu 

can form. Normal or insensitive points on the other hand should be 
those that have either surface roughnesses not large compared to a 
molecule, thus preventing a close packing of the adhering molecules, or 
those where the adhering molecules have such a loose packing as to leave 
places in the gas layer through which the oncoming ions can pass, and in 
so doing eventually perhaps clear the neighboring surface of the molecules 
adhering to it. 

It may be cited that, in agreement with this view, it is found that points 
with freshly ground or filed surfaces are in general not sensitive, whereas 
among points showing a large lag are those made smooth by fusion and 
zinc points made smooth by amalgamation (Gorton and Warburg, loc. 
cit.) and liquid points, whose surfaces are inherently smooth. Professor 
Kovarik informs the writer that when the usual method of making a 
steel point sensitive by fusion fails, a microscopic examination of the 
surface reveals the presence of a slightly raised scale of oxide formed by 
a crack in the otherwise glossy surface. 

There are some ways of making points sensitive, however, which 
cannot easily be reconciled with the idea that a smooth surface is always 
a necessary condition. Thus Gorton and Warburg (loc. cit.) found that 
a platinum wire could be made sensitive by heating to incandescence 
by the passage of an electric current, in which case the surface was not 
hot enough to smooth down slight inequalities by fusion. They also 
found that the sensitivity was produced when the wire point was thus 
heated in moist air or moist oxygen whereas when sensitive the point 
was reduced to its normal condition by heating in these gases after they 
had been dried by passage through sulphuric acid. 

A circumstance of significance is that on certain days it seems almost 
impossible to prepare a metal point showing sensitivity (when used in 
the open air), whereas at other times nearly every point shows more or 
less sensitivity. This behavior rather indicates that something gathers 
on the point surface which is more abundantly present in the atmosphere 
on some days than on others. Water vapor naturally comes to mind, 
but Edmunds (loc. cit.) observed lag in gases which had been well dried. 

Unless a wrong interpretation has been put upon the experimental 
evidence cited, none of the views presented gives a satisfactory explana- 
tion by itself of the lag phenomenon under all of the circumstances that 
are known to affect it. 

Some of the experiments to be described below give additional evidence 
on this problem, although others are also included in this paper which 
are of interest mainly from other considerations. 

In seeking for a possible effect of a surface layer, no attempt was made 



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NcJ'a?^^'] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. IO7 

to lcx>k for a very slight effect. The accuracy attainable in the measure- 
ments is usually not sufficient for distinguishing differences of less than 
one per cent, in the current or voltage which a change of conditions may 
produce. There are certain irregularities present in these discharges, 
especially noticeable with small negative currents, which often make it 
impossible to get exact repetitions of observations made with the same 
point. These very irregularities however point to some action at the 
surface. As the edge of the liuninous area on a negative point is observed 
through a microscope, certain irregularities of outline are seen to be con- 
stantly changing as if something more is taking place at the surface 
than the mere delivery of charges by the ions coming from the gas. A 
similar effect is noticed in the glow areas on the electrodes of discharges 
at low pressures. A spark often shows a reluctance to move from one 
portion of a metal surface to another. These effects as well as the lag 
phenomena which appear with sparks and discharges in tubes at low 
pressures are probably of the same character as those observed with point 
discharges. 

4. The amount of condensed gas upon a surface is generally supposed 
to depend upon the nature of the material of which the surface is com- 
posed, upon the pressure and the nature of the constituents of the gas 
itself, and upon the temperature; but Langmuir^ has recently brought 
forward evidence favoring a mono-molecular layer which for different 
materials varies in closeness of packing. 

Another factor which may possibly also enter into the problem is that 
the surface layer of gas on highly electrified points and even the density 
of the gas in the immediate neighborhood of such surfaces may be aug- 
mented by the attraction to which the gas molecules are subjected owing 
to their polarization by the strong field. A calculation shows that of 
itself this attraction is not sufficient to hold molecules against the surface; 
but when added to the forces already present which are capable of holding 
neutral molecules in position, it may for certain gases increase the number 
of molecules adhering to the siuiaces of some materials, at least. This 
argument fails if, as postulated by Langmuir (loc. cit.) we are to look 
upon each adhering molecule as held by a definite bond which it com- 
pletely satisfies in a classical sense. 

Precht^ found that coating a steel point with copper did not change 
either the voltage for which discharges commenced from the point or 
the magnitude of the currents at higher voltages, but Hovda' concludes 

* I. Langmuir, Am. Chem. Soc. Jour., 38, p. 2221; 39, p. 1848. 

« J. Precht Wied. Amialen 49. p. 150, 1893. 

' O. Hovda, Gottingen Inaugural Dissertation, 19 13. 



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I08 JOHN ZELENY, ^SS? 

from a long series of careful measurements that the voltages for which 
discharges begin do depend to a slight extent upon the nature of the 
metal. But doubt is thrown upon this conclusion by the fact that there 
were noticeable differences in the sharpness of the ends of the conical 
points which were used, diflferences whose effect could not be wholly 
eliminated and which may easily account for the small differences in 
the results obtained. 

Liquid Points. 

Some time ago the writer^ did some work on electrical discharges from 
a new class of points, consisting of minute hemispherical drops of water 
protruding from the ends of fine tubes. A method of measuring the 
electric intensity at the surface of the drops was devised and a study was 
made of the value of this intensity in air at atmospheric pressure, for a 
number of points differing in size. It was noted that the surface of the 
water becomes agitated when the electric current starts to flow from the 
point. For positive discharges this agitation is confined to small values 
of the current, the surface being quiescent for larger currents. A careful 
study was made later^ of these initial surface disturbances and it was 
shown that they arise from the surface becoming unstable when the 
electric intensity exceeds a certain limit. Under these conditions fine 
threads of liquid are rapidly pulled from the surface which break up into 
myriads of minute drops that act as carriers of the electric charge. When 
water, in air at atmospheric pressure, is used, the surface instability 
begins at a potential which is only a little below that at which the dis- 
charge would start from an undisturbed surface. For this reason the 
true cause of the surface disturbances was not discovered until some work 
was begun on discharges in other gases than air. 

The values of the electric intensities given in the paper first mentioned 
and the relation found for the dependence of these intensities upon the 
curvature of the discharging surface apply to conditions for surface 
instability rather than to the initial stages of the electric discharge, 
although for the smaller points the intensities for the two phenomena are 
almost identical. 

The electric forces at the surface of water points, when about to dis- 
charge positive electricity, which were indicated by those measurements, 
were considerably smaller than those found at the surface of platinum 
points by Chattock.' It seemed desirable therefore to repeat some of 
the measurements on the electric forces acting with discharges from liquid 

* J. Zeleny, Physical Review, 3, p. 69, 1914. 

'J. Zeleny, Proc. Carab. Phil. Soc., 18, p. 71, 1915; Physical Review, 10, p. i, 1917. 

*A. P. Chattock, Phil. Mag. (6), 20, p. 270, 1910. 



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Vol. XVLl 
No. a. J 



ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS, IO9 



points under conditions free from surface instability to ascertain whether 
these forces are actually different from those that obtain at the surfaces 
of similar metal points. The difficulty arising from surface instability 
may be avoided by working with air at reduced pressures, since in this 
way the discharge voltage is lowered while the voltage at which instability 
sets in is not affected. 

Apparatus for Discharges from LrguiD Points. 

6. The apparatus used for work on discharges from liquid points was 
arranged as shown in Fig. i. T is a brass cylindrical vessel 15 cm. high 




and 9 cm. in diameter. The outlets G, / and M at the left, lead to a 
pressure gauge, to the gas supply and to the pump respectively. A 
glass tube C passes through an insulating plug K in the upper end of the 
vessel and carries at its lower end the drawn out glass point L from which 
the hemispherical drop of liquid protrudes, the electrical discharge from 
which is under study. The brass disc P receives the discharge from the 
point and is connected to earth through a galvanometer. The glass 
tube C IS connected, by the rubber tube F, to the bottom of the movable 
reservoir £, the top of which is in turn connected by a similar tube D to 
the vessel T, Liquid extends continuously from the reservoir E to the 
drop at the end of L, and the height that the liquid surface in E is above 
the end of the point L is a measure of the pressure in the drop. The 
platinum wire B makes connection with the liquid in the system and 
leads to a Braun voltmeter and a battery of Leyden jars charged by an 
electrostatic machine. Some calcium chloride was kept in the bottom 



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no JOHN ZELENY. ^SS? 

of the vessel T so that water overflowing to the sides of the point, as 
often happened, would be removed by evaporation. The drop at the 
end of the point L was observed with a microscope through glass windows 
which are not shown in the figure. 

The distance from the tip end of a point to the plate opposite, which 
was 5 cm. in diameter, was 1.5 cm. in each case. This distance affects 
the voltage values but not the values of the surface electric intensities. 
The average temperature of the room was about 16** C. 

The fifteen points which were used in the experiments had radii ranging 
from 0.1 17 mm. to 0.988 mm., and were made from quill glass tubing 
which was drawn down to the proper diameter and broken squarely 
across from a fine scratch. The distilled water used was very slightly 
acidulated with hydrochloric acid to increase its conductivity, so that 
during a discharge there was no appreciable potential drop between the 
end of the liquid meniscus and the voltmeter. 

General Behavior with Liquid Points. 

7. The electric intensity / at the end of the drop is obtained from the 
distance p, that the liquid surface in E must be lowered to maintain 
the drop of the same form when charged as when uncharged, by means 
of the relation 

/ = ^Swpdg, (i) 

d being the density of the liquid. When the surface is not discharging 
a current, the electric intensity is not the same over the whole surface, 
being greatest at the tip end. To maintain equilibrium the shape of the . 
drop changes slightly from the hemispherical form. This does not apply 
to a surface discharging a positive current, for the current flows from the 
whole hemisphere (except for very small currents) and the intensity is 
found to be independent of the current density. 

A noteworthy feature of the discharge from water points in air at 
reduced pressures is the retardation in the commencement of the current. 
As the voltage of the point is gradually increased the current does not 
begin gradually, but rises more or less suddenly to a value of the order of 
a microampere. 

The retardation for any point is not constant in amount, but depends 
somewhat upon the age of the liquid surface and upon the time that has 
elapsed since a current last flowed from the point, and upon a chance 
element in the formation of ions in the gas as the applied voltage is 
raised. 

As has been stated in section i, a similar retardation in the current 



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Naaf^^*] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. Ill 

often occurs from metal points, which is larger and more frequently 
present with negative discharges than with positive discharges. But 
with many metal points the retardation is very small or not present, 
whereas with water points a retardation is the general rule. This 
retardation would in many cases be still larger than is observed were it 
not for the fact that a voltage is reached first at which the surface becomes 
unstable and the discharge starts owing to a disruption of the surface. 

When the current does start the water meniscus jerks back to a more 
flat position, because for the same voltage the electric pull is smaller 
with than without a current. 

After the current has started, the meniscus is quiescent with a positive 
discharge (but not with a negative discharge), and large changes in the 
magnitude of the current produce very little or no effect upon the electric 
pull upon the surface. (See end of section 12.) 

As, is the case with sensitive metal points in a lesser degree, the dis- 
charge current may be diminished below the value it suddenly assumed 
at commencement, and as the voltage is lowered to within about 50 
volts of the value at which the current would disappear if it kept on 
diminishing at its previous rate of diminution, the meniscus as a rule 
suddenly elongates and the current stops. The increase in the electric 
pull with diminution of voltage is so rapid during this final stage that it 
is extremely difficult to regulate both the voltage from the static machine 
and the liquid pressure necessary for maintaining the drop hemispherical, 
without having the water overflow to the sides of the glass tube. The 
most successful readings taken in this region showed that as the current 
fell to zero value, the total increase in the electric intensity as measured 
by the increase in the electric pull, may be as much as ten per cent, of 
the whole value. 

8. The retardation which has been discussed, occurs both with positive 
and negative discharges, and accordingly it is not possible to get any 
very definite voltages nor surface electric intensities for which currents 
begin to flow from these points.. 

It is possible however to obtain definite values for the electric intensities 
at the surface of points from which positive currents above a certain 
minimum are flowing, and to obtain the voltages for which these currents 
stop; and this has been done. Such measurements cannot be made 
with negative discharges because with them the surface of the liquid is 
agitated, owing to an intermittent element in the current and to the fact 
that the negative discharge is confined to a minor portion only of the 
surface. Often with some of the larger negative currents, however, the 
surface becomes almost quiescent. 



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112 JOHN ZELENY, ^^SSSS. 

As explained above, the electric intensity at the surface of a point 
changes but little with the current except just as the current is about 
to stop, where its value rises rather rapidly about lo per cent. The values 
which will be recorded were taken in the region of small currents where 
the intensity begins to be constant in magnitude, but they apply equally 
well to larger currents. , 

The range of pressures that could be employed in the experiments was 
limited, on the lower side, by the pressure (about lo cms. of mercury) 
at which the water commenced to vaporize in the upper portion of the 
glass tube ; and on the upper side, by the value for which the discharge 
voltage was smaller than the voltage for which the surface became 
unstable. For the smallest points, observations could be made up to 
atmospheric pressure but this pressure could not be reached with the 
larger points. Owing to experimental difficulties the limits mentioned 
were not always attained. 

Electric Intensity at Surface during Positive Discharge. 

9. The electric intensity at the surface of a point discharging a small 
positive current was determined for each point for a number of air 
pressures by the method previously explained. The results for some 
of the points expressed in electrostatic units per cm. are plotted as broken 
line curves in Fig. 2 against pressures expressed in centimeters of mercury, 
the radius of the point in millimeters being indicated on each curve. 

From the whole set of these curves, the full line curves in Fig. 2 were 
constructed, each giving the relation between the electric intensities 
and the radii of the points, for the air pressure affixed to the curve. 
It is seen that the intensity diminishes as the radius of the point increases, 
the rate of change being most rapid for the smallest points. An explana- 
tion of this fact is given in section 19. 

Empirical Relations. 

10. The relations shown by the whole set of curves in Fig.- 2 is expressed 
very well by the equation 

/ = 0.955 /> + 5.60^-, (2) 

/ being given in electrostatic units per cm. when p is taken in centimeters 
of mercury and r in centimeters. 

An approximate formula of this form was obtained by Edmunds^ for 
the field at the surface of a point at the commencement of a discharge 

> p. J. Edmunds, Phil. Mag. (6), 28, p. 234, 1914- 



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No!"2^^^*] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. I 1 3 

(positive and negative not distinguished) between a point and a plane, 
who adapted to this case Townsend's method for coaxial cylinders, in 
which use was made of the empirical relation found by Bailie for the 



PR£33tM^ 20 




Fig. 2. 

Electric intensities at surfaces of water points during positive discharge. Dotted line 
curves show the variation of the electric intensity with air pressure for individual points whose 
radii are given in millimeters. Full line curves show the variation of the electric intensity 
with size of points at constant air pressure expressed in centimeters of mercury. 

dependence of the sparking potential between parallel plates upon the 
distance between them. 

The constants in the formula as derived by Edmunds give values of / 
which are from 20 to 30 per cent, larger than those here determined with 
a current flowing. 

II. Equation (2) may be written as 

ir = 0.955 pr + 5.60 Vpr, (3) 

showing that /r is a function of pr only. By taking different values of 
p and r whose products are constant, the products of the corresponding 
values of / and r are also constant. An illustration of this relationship 
is given in Table I., the data for which were taken from the curves in 
Fig. 2, a value of r being chosen from each pressure curve which gives the 



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114 



JOHN ZELENY. 



COND 



constant product of pr placed at the top of each set of numbers, and the 
value of / corresponding to this value of r being read from the curve. 
The last column indicates the degree of constancy of fr for each case 
considered. 

Table I. 



/r « o.pxa. 




>r-a 


.8. 




r. 


/. 


/. 


A. 


r. 


>. 


/. 


A. 


.012 


76 


520 


6.24 


.0368 


76 


318 


11.7 


.0152 


60 


413 


6.28 


.0466 


60 


255 


11.9 


.0182 


50 


342 


6.22 


.0560 


50 


210 


11.8 


.0228 


40 


270 


6.16 


.0700 


40 


171 


12.0 


.0304 


30 


202 


6.14 


.0933 


30 


128 


11.9 


.0456 


20 


134 


6.11 











Taking the average values of fr thus obtained and plotting them 
against the corresponding values of pr we get the experimental relation- 
rp 1 2 3 d 5 

17 



15 
f3 

If 
9 

7 











10 
£SU/t>n 


£5 


40 




70 On 


J 




Mm. 
JOT. 














S50 


>^ 


iT 




y 


y 
















O mtt^A/mlmt 


9000 


\ 












y 


V 


y 


X 




.i^ 


\ 




E? 








\ 


M3. 




\ 










too 


X 


y 




/ 


^ 








V 


-^ 


__ 




loots 


>,0 4 


o t 


\0 & 


^ y^ 






1^ 


Y 




IWu 






/ 


y\ 






/ 


y\s. 






3000 




/ 


/ 






/ 


Y 










/ 


r 






/ 


f 






\jooo 



Cm. 20 



40 



& 



Fig. 3. 

Curve I. represents the relation between rf and rp, r being in millimeters, p in centimeters 
of mercury and / in electrostatic units per cm. The crosses are experimental values and the 
circles values computed by equation (3). 

Curves II. and III. show the variation with pressure expressed in centimeters of mercury 
of the constant a in equations (4) and (5) respectively, when v is in volts and r in millimeters 

Curve IV. shows the variation with pressure of the constant b in equation (5), expressed 
in millimeters. 

Curves V. gives the electric field in e.s.u. per cm., during positive discharge in air at diff- 
erent pressures expressed in centimeters of mercury, at the surfaces of the three liquids 
named for a point of 0.346 mm. radius. 



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No'a?^^] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. II5 

ship shown by the crosses on curve I. in Fig. 3, which combines in one 
curve the data represented by all of the curves in Fig. 2. With the aid 
of curve I., it is possible to find the value of the intensity / which applies 
to a point of any radius in air at any pressure, within the limits used in 
the experiments. The points marked by circles on Curve I. represent 
values obtained from equation (3), and show the degree of exactness 
with which the equation respresent the experimental values. 

12. Now Townsend^ has already shown that it follows from the theory 
of ionization by collision that if the same number of ions is produced by 
collision in two similar systems the product fr must be constant for all 
conditions where pr is constant, it being presupposed that the current 
flowing is sufficiently small for the volume charges present not to affect 
the field appreciably; and that this relation holds for the critical fields 
required to start discharges from metal points has been shown by 
Edmunds^ and by Tyndall.* 

The work just reported proves that the product fr remains constant 
for constant values of pr not only for the case where the current is the 
same and small as is contemplated in Townsend's theorem, but irrespec- 
tive of the magnitude of this current. This follows from the constancy 
of/ for all currents above a certain minimum value. This constancy of 
the surface field/ for all values of the current indicates that any increase 
of this field owing to an increase of applied voltage is compensated by a 
diminution arising from larger volume charges present in the gas with the 
larger currents. 

The nicety of this compensation is hardly fortuitous and it is probable 
that when this limiting field exists at the surface the electric forces in the 
space where ionization takes place have reached a value such that a 
slight change in field results in a large increase in the number of ions 
produced and hence as the voltage of the point is raised nearly the whole 
of the change goes to strengthen the field beyond the main region of 
ionization, this being necessary for the removal of the increased number 
of ions produced. This process does not continue indefinitely for the 
glow discharge eventually changes into a brush or spark discharge. 

Comparison of Fields with Metal and Liquid Points. 

13. Only one result for the field strength at the surface of a metal 
point during positive discharge is available for direct comparison with 
values obtained at a water surface. This is found in a paper by Chattock* 

> J. S. Townsend. The Electrician. 71. p. 348, 1913. 
* P. J. Edmunds. Phil. Mag. (6), 38. p. 334, 1914. 
•A. M. Tyndall, Phil. Mag. (6). 30. p. 640, 1915. 
*A. P. Chattock, Phil. Mag. (6). 20, p. 273. 1910. 



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Il6 JOHN ZELENY. [USS! 

where a table is given from which the field at the surface of a platinum 
point of 0.18 mm. radius in air at atmospheric pressure (exact pressure 
not stated) with a positive discharge current of 0.79 microamperes is 
computed to be 413 e.s.u. per cm. as compared with 426 e.s.u. per cm. 
obtained for a water point of the same radius (as shown in Fig. 2). 

A more extended indirect comparison may be made by making use of 
the critical fields determined at the surfaces of metal points when a 
current starts or stops. Such critical fields were obtained for a number 
of platinum points at atmospheric pressure by Chattock (loc. cit.) and 
the results embodied in an empirical equation, /r^** = 85 (/ in e.s. units 
per cm. and r in cms.); and Tyndall's more recent paper (loc. cit.) 
shows the values of these fields at different pressures as well. The 
critical fields were computed from the square roots of the electric pulls 
on the ends of the points. A table in Chattock's paper (p. 273) shows 
that the square roots of these pulls is 7 per cent, greater as the current 
stops than it is with a current of the order of a microampere, and a 
curve in Tyndall's paper shows a difference of 11 per cent, for the same 
thing. The average of these values (9 per cent.) will be used for making 
the reduction. 

There is an additional correction to be made. When a current flows 
from all parts of the hemispherical end of a cylindrical wire, which is 
the case for positive currents above a few microamperes, the electric 
intensity is the same over the whole surface and may be obtained directly 
from the electric pull on the surface. But when a current just ceases to 
flow, the electric intensity is greatest at the tip end of the wire, and to get 
the intensity at this place a correction of 8.5 per cent, must be added to 
the average value found from the electric pull, as was shown by Young.^ 
This correction is included in the values of the critical fields represented 
by Chattock's empirical formula, and presumably also included in 
Tyndall's values. The critical fields for which a current stops may 
therefore be obtained approximately, by increasing by 17.5 per cent, 
the fields computed from the square roots of the electric pulls measured 
when a current above a certain minimum value is flowing. 

Now the values of the critical fields computed by Chattock's formula 
are on the average about 15 per cent, larger than those shown by the 
curve for atmospheric pressure in Fig. 2, the difference being somewhat 
larger than 15 per cent, for the smallest points indicated on that curve 
and smaller than 15 per cent, for the largest points. On the other hand 
the values of the critical fields taken from Tyndall's curve are uniformly 
larger by about 13.5 per cent, than corresponding fields given on Curve I. of 

» F. B. Young. Phil. Mag. (6), 13. p. 542, 1907. 



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NSTa^^'l ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. II7 

Fig. 3 for liquid points with a current flowing. This indirect comparison 
shows therefore an average difference of over 3 per cent, between the 
results for metal points and those for liquid points, which is the same as 
that found above in the direct comparison made with the single result 
available for metal points. Considering all of the circumstances, great 
weight cannot be placed upon a difference of this magnitude, and it can 
only be said that if afty difference exists between the fields during positive 
discharge, at the surface of a platinum point and a water point of the 
same radius, this difference is small. 

Stopping Voltages for Positive Discharges. 

14. The procedure followed in obtaining the stopping voltages was as 
follows. The current flowing from the point was measured for a number 
of decreasing voltages down to the one foi which the water drop suddenly 
overflowed owing to the rapid increase of the electric pull. From these 
values the voltage was found graphically for which the current would 
have vanished if it had followed the previous rate of decrease. The 
voltage thus obtained was usually less than 100 volts below the last 
reading actually taken. 

The experimental results on the voltages at which positive dis- 
charges ceased in air at different pressures are shown by the curves in 
Fig. 4. The two broken curves show the relation between the stopping 



PfTESSURe go 




Fig. 4. 
Stopping potentials in volts for positive discharges from water points of different radii 
expressed in millimeters, in air at different pressures given in centimeters of mercury. Dis- 
tance to plate - 1.5 cm. 



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Il8 JOHN ZELENY. l^SS? 

voltages and air pressures as obtained for two of the points whose radii 
are indicated on the curves. 

It seemed preferable to plot all of the voltage-pressure results as radius- 
voltage curves and these are drawn in the figure as full line curves. Here 
each curve corresponds to a given pressure, whose value in centimeters of 
mercury is affixed, and represents the dependence of the stopping voltages 
upon the radii of the points used. The values for these curves were 
taken from the complete set of voltage-pressure curves similar to the 
two broken line curves shown in the figure. 

The voltages at atmospheric pressure were obtained in the region 
bordering on the state of surface instability but they agree within experi- 
mental errors with results obtained previously^ for positive discharges 
in air at the same pressure from the same sized points made of brass. 

15. The radius-voltage curve for each pressure in Fig. 4 may be repre- 
sented equally well by either of the two empirical relations, 

v = a^r + b (4) 

or 

V = a^r + b, (5) 

V being the stopping potential, r the radius of the point, and a and b 
constants. 

The term b in equation (4) is small compared to the second term and 
hence its value is not obtained accurately. The numbers found for it 
from the different curves showed no regular tendency to vary with the 
pressure, and so the average value 340 volts,* was taken as common to 
all of the curves, and values of the constant '*a" were found on this 
assumption. These values of a, for r expressed in millimeters, are plotted 
against the corresponding air pressures expressed in centimeters of 
mercury as curve II. in Fig. 3. 

In equation (5), both of the constants a and b are dependent upon the 
pressure of the ain Values obtained for the constant a are shown by 
curve III. in Fig. 3 and are seen to follow in general the values of the 
corresponding constant in equation (4), represented by Curve II. The 
values of the constant^ b vary from .072 to .032 mm., decreasing as the 
pressure increases, and are shown by Curve IV. in Fig. 3. Obviously a 

» J. Zeleny, Phys. Rev.. 25, p. 313, 1907. 

' This constant may be interpreted to signify the lowest potential at which a discharge 
can occur; and its value is actually within a few volts of the minimum spark potential ob- 
tained for air by Strutt (341) and by Carr (350). 

* A physical meaning which may attach to this constant b, is that the effective radius of 
the point in the discharge is greater by this value than the real radius, which would be the 
case if for example the region of the luminous glow (whose thickness increases as the pressure 
is reduced) were highly conducting. 



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Vol. XV1.1 
No. 2. 



'] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. I I9 



combination of equations (4) and (5) would represent the experimental 
results equally well or better, and would involve quantities having the 
significance of both of the constants b in the two equations. It is to be 
noted that at the higher pressures the stopping voltages for the larger 
points become approximately proportional to the square roots of the 
radii of the points. 

Fields in Different Gases. 
16. The electric intensity during positive discharge at the surface of a 
water point was also measured at different pressures in the gases, carbonic 
acid, hydrogen and oxygen, as well as in air. The general behavior of 
the discharge in these gases was similar to that found for air. The 
electric intensity at the discharging surface was found to be very nearly 
independent of the magnitude of the current, but in oxygen the discharge 
was less steady than in the other gases, especially with small currents,, 
the liquid surface becoming quiescent only after the current approached 
about two microamperes. The numerical results given in Table II.. 
were taken from curves drawn through the experimental values obtained^ 
The different upper limits of pressures used are imposed by surface 
instability. No simple relation is apparent between these values and 
other related quantities. 

Table II. 

Electric Intensities (in E.S.U. per cm.) at Water Surface during Positive Discharge in 

Different Gases. 



Radios of Point » 0.346 Mm. 


Radius of Point » o.i6a Mm. 


Pressure of Gas in 
Cm. of Mercury. 


CO,. 


Air. 


H. 


0. 


CO,. 


Air. 


10 
20 
30 
40 
50 
60 
70 
87 


157 
205 
248 
286 


117 
155 
191 
225 

255 
283 


97 
128 
155 
180 
203 
225 
246 
277 


183 
212 
239 
270 


250 
330 
387 
436 


189 
238 
281 
325 
367 
397 



Fields for Different Liquids. 
17. Some experiments were made with a point of radius 0.346 mm. 
using the liquids water, glycerine and methyl alcohol in succession in 
air at different pressures, in order to determine whether the nature of 
the liquid has any effect upon the electric field at the surface during a 
positive discharge. The behavior of the discharge with glycerine and 
methyl alcohol was in general the same as has been described for water^ 



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I20 JOHN ZELENY. [^5»? 

but both liquids were even more difficult to work with than water. The 
experimental errors in the measurements with these liquids were therefore 
greater than was the case with water. 

The results of the measurements made are shown by Curve V. in Fig. 3, 
and it is seen that the three sets of points fit one curve within the experi- 
mental error with the possible exception that the values for methyl 
alcohol are somewhat low at the highest pressures used with this sub- 
stance. Owing to the great difficulty of making measurements at all 
in this region, which is near the instability voltage for methyl alcohol, and 
owing to the fact that at lower pressures the results for this liquid are 
in agreement with those for the other liquids it is believed that there is 
no significance in the slightly lower values obtained with methyl alcohol 
for pressures above 30 cms. 

A comparison was also made, over the same range of pressures as used 
above, of the voltages at which the positive discharge stopped from the 
three liquids and from a metal point made of brass wire with a rounded 
end of the same radius as that of the liquids. Here again no difference 
above the experimental error was found between the different substances 
with the same exception of the values for methyl alcohol above 30 cms. 
pressure which were again below those for the other substances. 

Metal Point Coated with Various Substances. 

18. In seeking evidence of the possible effect of the nature of the 
material of which a point is made, upon the potential at which a discharge 
starts from it, experiments were done in which a brass point (diameter 
= 0.5 mm.) was used when coated in succession with different substances, 
including cadmium sulphate, thorium oxide, potassium iodide, caustic 
potash, fluorescein, methyl violet and the chlorides of sodium, tin, copper, 
mercury, iron and cobalt. It was not possible in general to get a thin, 
uniform coat of the material on the point, either by evaporation from 
solution or by application in the form of a fine powder or by fusion, but 
notwithstanding this unevenness of the surfaces, the potential at which 
positive discharges started and stopped from the coated points was 
approximately the same throughout as from the uncoated point. The 
total variation among the results was about two per cent, which is some- 
what greater than twice the experimental error of the voltage determina- 
tions. Within the limits named, therefore, the positive starting potential 
is independent of the nature of the material of which the point is made and 
equally independent of a considerable roughness of surface. 

With negative discharges, however, the starting potentials showed a 
total variation of about 25 per cent., the values ranging on both sides 



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NoiTa^^^l ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. 121 

of the value for the positive discharge.^ Without more evidence, this 
behavior should be ascribed not to the influence of the material of the 
surface but rather to the effect of its inequalities, the greater localization 
of the negative discharges making such inequalities of moment for these 
discharges. 

Discussion of Fields at Surfaces having Different Curvatures. 

19. It is surprising at first sight that the surface field intensity required 
to start and maintain discharges should be the larger the smaller the 
radius of curvature of the point, but an explanation of the fact is found 
on the theory of ionization by collision by considering the nature of this 
process and the character of the field in the neighborhood of such surfaces. 

The field intensity near the surface of points decreases very rapidly 
with distance from the surface, and the decrease is the more rapid the 
smaller the radius of curvature of the point. For illustration consider the 
nearly analogous case of two charged spheres, one of radius o.oi cm. and 
the other of radius o.i cm. For the smaller sphere, the field at a distance 
of 0.01 cm. from the surface is only 25 per cent, of its value at the surface 
and at a distance of 0.04 cm. it is but 4 per cent. For the larger sphere, 
however, the fields at the same distances from the surface are 82 per cent, 
and 50 per cent, respectively of the value at the surface. 

Now ionization by collision does not begin abruptly at a definite field 
strength, but owing to the chance elements entering, the process is a 
statistical one and hence if there is an appreciable rate of increase of ions 
by this process in the field at the surface of a point there must be an 
appreciable though smaller rate of increase at a distance from the surface 
where let us say the field is but half as strong. 

Consider two points of different size so charged that the field intensities 
at their surfaces are the same, and imagine the same number of ions drawn 
toward each surface from the surrounding gas. Consider the multi- 
plication of these ions in volume elements formed by equi-distant surfaces 
parallel to the surfaces of the points. In the two volume elements 
adjacent to the surfaces of the two points the rate of increase of the ions 
will be the same because the fields there are assumed to be equal but in 
all of the following volume elements the rate of increase will be larger 
for the point of larger radius of curvature because for this point the field 
strength falls off less rapidly with distance. Accordingly the total num- 
ber of ions reaching the larger point per second will be greater than the 
number reaching the smaller point, and it follows that, in order to have 

* For a point of this diameter the normal starting potential is the same for the two kinds 
of discharges. See J. Zeleny. Physical Review, 25, p. 305, 1907. 



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122 JOHN ZELENY. ^Siu 

ions reach the two point surfaces at the same rate, not so large a field 
intensity is necessary at the surface of the larger point as is required for 
the smaller point. It is thus made apparent why the field strength at 
the discharging surface is not the sole determining factor for the produc- 
tion of a discharge and that the manner in which the field changes with 
distance from the surface is of much importance; the field at the surface 
being least when the field is uniform and increasing more and more as 
the divergence of the field increases. 

In discharges between a cylindrical wire and a concentric cylinder the 
field at the wire changes less rapidly than it does at the end of a wire of 
the same diameter, and accordingly the critical field required to start a 
discharge should be less in the former case than in the latter case. Wat- 
son^ has computed the critical fields at different pressures at the surface 
of the inner of two concentric cylinders from the critical discharge 
voltages. The smallest wires he used correspond to the largest of those 
given in Fig. 2 and for these the values are almost identical with those 
of the figure named, showing when the correction discussed in section 12 
is applied that the field at the cylindrical wires is about 17.5 per cent, 
smaller than for points of the same diameter. 

Effect of Divergenxe of Field. 

20. The effect of the divergence of the field at the surface upon the 
intensity of the field that obtains there during a discharge, is well illus- 
trated by the following experiment in which the divergence of the field 
near a given point was artificially altered. 

A small ring, 5 in Fig. i, 4 mm. in external diameter, made of wire I 
mm. in diameter, was held by a vertical stem so that it surrounded the 
glass point U used (diameter = 0.53 mm.). The ring was adjustable 
vertically and was metallically connected to the liquid inside the point. 
The presence of this ring near the end of the point made the field at the 
point less divergent by an amount which depended upon its vertical 
position, the effect being greater the lower the ring. The electric in- 
tensities, /, at the surface of the point obtained when a positive discharge 
was passing in air at a pressure of half an atmosphere for different dis- 
tances, d, that the tangent plane through the lower surface of the ring 
was above the end of the discharging point are given in Table III. 

Table III. 

/. 

2.0 mm. 249 e.s.u. per cm. 

0.34 236 

0.10 218 

0.026 212 

0.00 201 
« E. a. Watson. The Electrician, Feb. 11. 1910. 



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Naa?^^*l ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. 1 23 

The voltage required to maintain a current was increasingly larger 
as the ring was lowered, but the intensity at the surface became smaller 
and smaller as the field was made less and less divergent by changes in 
the position of the ring. The experiment was repeated at other air 
pressures with a like result and confirms the reasoning in the last section. 

Comparison of Currents from Surfaces of Different Materials. 
21. Since the velocity with which the ions impinge against thesurface 
of a discharging point is large, it is possible that the impacts may liberate 
other ions from the surface which may appreciably increase the current 
due to the ions produced in the volume of the gas. If such is the case, 
it is probable that the number of ions so ejected by a given number of 
impacts should depend upon the material of which the point is made, 
and accordingly if similar points made of different materials are used the 
current obtained with the same voltage should not be the same from the 
different points. As already stated (Sec. 3) Precht found that after 
plating a steel point with copper the current obtained with a given voltage 
remained unchanged. Additional experiments were made on this subject 
by obtaining the voltage-current curves for both positive and negative 
discharges in air from points with rounded ends made of platinum, copper, 
brass and water. The points were used at a distance of 1.5 cm. from a 
plate and all had a common diameter of 0.41 mm. After a slight correc- 
tion for differences in atmospheric pressure was applied, the results with 
positive discharges from the different materials were identical within 
experimental error. For negative discharges also, the metals gave iden- 
tical results. The negative discharge from the water point produced an 
agitation on the surface. This became less violent as the current was 
increased until when the voltage was between 7,000 and 8,000 volts 
(starting voltage being 4,700) the surface was almost quiet and showed 
a hazy edge only under the microscope, owing to a small amplitude 
oscillation. Under these conditions the current from the water point 
was a little smaller than that obtained with the metal points, so that for 
example 7,600 volts was required on a water point to produce the same 
current as was obtained with 7,500 volts when the metal points were 
used: This small difference may be explained by any one of three causes. 
Either electrons are ejected in smaller number from a water surface than 
from a metal surface during the discharge, or the smaller currents with 
water are due to the changes in the shape of the point caused by the small 
oscillations present, or the reduction in current from water points arises 
from a diminution in the mobility of the negative ions owing to the pres- 
ence of water evaporating from the point. On the whole, the results 



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124 ^^^^ ZELENY. IsSnS! 

indicate that if any ions are ejected at all from the surface by the impact 
of approaching ions, the number of such ions must be small compared 
with those producing them; unless indeed owing to the influence of 
volume electrification the currents from points in general are controlled 
almost entirely by the applied voltage and but slightly by the number of 
ions produced in the neighborhood of the point. 

Discussion. 

The ideal smoothness of liquid surfaces favors their use for the investi- 
gation of a possible surface action in point discharges, since with metal 
points the physical state of the surface and in most cases its chemical 
composition as well is a matter of constant concern, mainly because of 
the changes wrought by the discharges themselves. 

Unfortunately the chemical composition of these liquid surfaces also 
was subject to change as evidenced by changes in surface tension. The 
action of a discharge appears to cleanse the surface, since the value ob- 
tained for the surface tension was always largest after a discharge and 
gradually diminished with time. It is possible that some of this surface 
ageing is to be attributed to the adsorption of gas molecules by the surface. 
While all of the liquids used showed a lag in starting for both positive 
and negative discharges, the amount of lag observed for any point may 
vary greatly on different trials, and it is probable that this fact is to be 
ascribed to the changes in surface composition, just noted. 

The general presence of lag with liquid points lends support to the 
working hypothesis that the lag phenomenon is dependent upon a com- 
pact non-conducting layer of molecules upon the surface, since the smooth 
surfaces are favorable for the formation of such layers. The comparisons 
made of surface electric intensities during positive discharges show these 
to be virtually independent of the material of the surface, and hence it 
may be assumed that any non-conducting layers which may have been 
present at the start have under these conditions been removed. 

Further discussion of the results given in this paper are reserved until 
some other experiments which have been made are reported in a second 
paper. 

Summary. 

Considerations are given for attributing the lag phenomenon in point 
discharges to the presence of a non-conducting coating on the discharging 
surfaces which may consist of adhering gas molecules. 

Both positive and negative point discharges from surfaces made of 
water, glycerine or methyl alcohol show a lag in starting. 

The electric intensity / at the surface during positive discharges is 



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No'a?^^^*] ELECTRICAL DISCHARGES FROM POINTED CONDUCTORS. 1 25 

practically 'independent of the current and of the material of the point. 
For water points / (e.s.u.) is related to the point radius r (cm.) and the 
air pressure p (cm. of mercury), by the relation fr = 0.955 P^ + 5-6o V^. 

The stopping voltages v for positive discharges from water points of 
radii r may be expressed by either v = a^lr + b or v = a^lr + b where 
a and b are constants for any pressure and have been obtained for a 
number of pressures. 

The surface electric intensities during positive discharges in air, hydro- 
gen, oxygen and carbonic acid at different pressures are given for two 
different points. 

Coating a metal point with various substances was found to affect very 
little the potential at which positive discharges commenced whereas 
the effect upon the potential for the negative discharges was large, but 
this may be due to the unavoidable roughness of the surfaces used. 

The influence upon the discharge of the divergence of the electric 
field at the discharging surface is shown to explain the fact that the field 
necessary for a small point is larger than for a large point. 

Ejections of ions from a surface by the impact of other ions is made 
improbable in point discharges from a study of the voltage-current rela- 
tion from surfaces of water, platinum, copper and brass. 

Sloans Laboratory, 

Yalb University, ' 

March 29, 1920. 



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126 L, R. INGERSOLL AND OTHERS. [toSS 



SOME PHYSICAL PROPERTIES OF NICKEL-IRON ALLOYS. 

By L. R. Ingbrsoll and othbrs.i 

Synopsis. 

The specific heats, thermal conduaivities, thermoelectric powers, and specific re- 
sistances have been determined for a series of iron-nickel alloys of exceptional purity 
and definitely known composition. 

The specifi(i heat (25® to 100** C.) varies only slightly with change in composition, 
but gives, nevertheless, a well defined maximum at 35 per cent, nickel. The thermal 
conductivity (30^ to 100® C.) on the other hand, shows a much larger variation, 
with a value for 35 per cent, nickel of only one fifth of that for either pure iron or 
pure nickel. The thermoelectric power (o® to 96^ C.) against copper exhibits a 
marked minimum at 35 per cent, nickel with maxima at about 20 per cent, and 
So per cent. The specific resistance at o** C. shows a marked maximum at 35 per cent, 
nickel, more than five times the value for either pure iron or pure nickel. The 
relative increase is not so great as the temperature is raised to 700** C. The tem- 
perature coefficient of resistance, considering the whole range (o® to 700® C), is a 
minimum for the 35 per cent, nickel. 

These facts are in general agreement with the anomalies in other properties 
shown by nickel-iron or nickel-steel of this composition and point to the formation 
of the definite compound FeiNi. 

WHILE nickel-iron and nickel-steel alloys have been very ex- 
tensively investigated* as regards their mechanical, magnetic 
and similar characteristics of practical interest, other properties of equal 
importance to the physicist have been little studied. It is true that 
K. Honda' has measured the thermal (as well as the electrical) conducti- 
vities of a series of nickel steels, and W. Brown* the specific heats for a 
number of specimens containing up to 31 per cent, nickel, but no attempt 
has been made in the way of determining and correlating these and other 
physical properties for the same series of specimens. 

In an extended research on the properties of alloys of iron with nickel 
and copper, carried out in the electrochemical laboratory of the Uni- 
versity of Wisconsin some years ago, a considerable number of ferro- 
nickels were produced. These formed a graded series, of nickel content 

^The measurements for this work were carried out at various times by Messrs. O. F, 
Mussehl. D. L. Swartz, H. F. Smith, C. G. Thompson, M. A. Mahre and Misses J. F. Fred- 
erickson and D. R. Hubbard, working under the direction of Professor Mendenhall, Pro- 
fessor Terry or myself. 

' Vide Bureau of Standards Circular No. 58 for a r6sum6 of such work. 

• Tohoku Univ. Sci. Reports, 7, 59. 191 8. 

* Roy. Soc. Dublin, Trans., 9. 6, 59, 1907. 



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Voi« XVLl 
No. 3. J 



PHYSICAL PROPERTIES OF NICKEZ^IRON ALLOYS, 



127 



varying from i to 90 per cent., and of such purity of material and defin- 
itely known composition as to afford a rather unusual opportunity for 
experimental studies of the sort described here. They were furnished 
through the kindness of Mr. James Aston, by whom, in connection with 
Professor C. F. Burgess, they had been made and their mechanical and 
electrical properties studied.^ These showed unusual changes when the 
nickel content was between thirty and forty per cent. — in keeping with 
the remarkable properties of 35 per cent, nickel-steel, e.g.^ invar. It 
seemed of importance, then, to determine if the same was true of certain 
other of their physical properties and accordingly their specific heats, 
thermal conductivities, thermoelectric powers and resistances as a func- 
tion of temperature have been studied in this connection. 

Table. 



Alloy. 


Percent 
Nickel. 


SpecUlc Hett 
as-xoo* C. 

(om.)' 


Thermel 

CondQctirity 

ao-xoo'*C. 

(C. 0. s. 

Unite). 


Thermoelectric 
Power (Acainst 

S3??! 

/MicroTOlte\ 
V Deg.'^C. /• 


Specific Re- 
■iitence ao ^C. 
/Microhmt\ 
\ Cm.«. I' 


Tempemture 

CoMcient of 

Rei. o-xoo °C. 


Fe 







.1428 








144E.... 


1.07 


.1162 


.1035 




.... 


.... 


144F.... 


1.93 


.1170 


.1009 




.... 


.... 


150J.... 


4.0 


.... 




2.32 


20.9 


.0020 


150L.... 


7.0 


.... 


.... 


7.32 


25.2 


.0023 


144J.... 


7.05 


.1163 


.0727 


. . • . 


.... 


.... 


157D.... 


10.20 


.1168 


.0687 




.... 


.... 


166A.... 


13.0 


.... 


.... 


16.9 


33.0 


.0018 


144M.... 


13.11 


.1160 


.0534 


.... 


.... 


.... 


166B.... 


14.0 




.... 


17.2 


33.9 


.0016 


166E.... 


18.0 


.... 




21.0 


35.9 


.00084 


144P.... 


19.21 


.1163 


.0502 


.... 


.... 


.... 


150S.... 


21.0 




.... 


23.5 


38.8 


.0018 


166G.... 


22.11 


.1163 


.0490 


21.0 


40.0 


.0018 


1S4S.... 


25.20 


.1181 


.0320 


.... 


.... 




1661 


26.40 






16.7 


35.9 


.0016 


166C.... 


28.42 


.1191 


.0278 


.... 




.... 


166L.... 


35.09 


.1228 


.0262 


9.79 


92.0 


.0011 


166M . . . 


40.0 


.... 


.... 


22.4 


74.1 


.0022 


166N.... 


45.0 


.... 




29.0 




.... 


1660.... 


47.08 


.1196 


.0367 


31.9 


47.5 


.0036 


166Q.... 


75.06 


.1181 


.0691 





.... 


.... 


173W . . . 


90.0 


.... 


.... 


17.9 


15.5 


.0034 


Ni 


100.0 


.1168 


.1402 


.... 


.... 


.... 



Alloys. — The alloys had been prepared with the aid of a resistor furnace 
by melting* weighed amounts of iron and nickel in a magnesia crucible 

> Met. & Chem. Eng., 8, 33, 1910. 

'For a more detailed description of this process see Univ. of Wis. Bull. No. 346, Eng. 
Series. Vol. 6, No. 2. p. 6. 



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128 L, R. INGERSOLL AND OTHERS. [^S^ 

supported by a graphite jacket. The iron was obtained by a process 
of double electro-deposition and was 99.97 per cent. pure. The nickel 
was also electrolytic material of high purity. The resulting ingots, 
which weighed about 500 g. each, had been forged into rods and then 
machined into bars about i cm. in diameter. In the case of most of the 
specimens tested, the exact composition had been determined by chemi- 
cal analysis, and the close agreement of the analytical results with the 
percentage of nickel added to the charge may be taken as evidence of 
the perfect alloying of the iron and nickel. The carbon content was 
estimated at considerably less than o.io per cent. 

As will be noted on inspection of the table, the series of specimens 
on which the specific heat and conductivity measurements were made 
was not identical with that on which the other experiments were per- 
formed. While this is perhaps to be regretted, the fact that all these 
alloys were made in exactly the same way and of materials of the same 
purity, practically does away with any objection arising from this cir- 
cumstance. It may be remarked that the specimens for which the 
nickel content in the table is given to two decimal places (e.g., 22.11 
per cent.) are those for which an exact analysis had been carried out. 
The composition of the others (e.g., 13.0 per cent.) was determined from 
the amounts of materials used in forming the alloy and hence it is not 
so accurately known. 

Specific Heat. — The specific heats were determined by means of a 
Joly steam calorimeter, using a delicate Sartorius balance. Before 
testing, samples of the alloy which weighed about 38 grams each were 
annealed by packing them in iron filings in an electric furnace and heating 
to 900° C. for over an hour, then cooling very gradually. The specimens 
were then carefully polished with various grades of emery paper. Three 
different sets of measurements were made, all of which gave results in 
excellent agreement. The mean values only are included in the table 
and plotted in Fig. i. 

The results are in good agreement with the measurements of Brown, 
already mentioned, although he did not investigate specimens with 
more than 31.4 per cent, nickel. The maximum in the curve at 35 per 
cent, nickel is very marked although the actual change in specific heat is 
small. 

Thermal Conductivity. — This was determined by the well-known method 
of Gray.^ ,The specimens used were those for which the specific heats 
had already been measured. They were between 5.1 and 6.7 cm. in 
length and of an average diameter of about .98 cm. To minimize losses, 

* Proc. Roy. Soc. London, 56, 199, 1894. 



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NoTa?^^'*] PHYSICAL PROPERTIES OF NICKEL-IRON ALLOYS. I 29 

the copper ball, to which the heat was conducted, was surrounded by a 
jacket through which flowed water at room temperature. The rod 
itself was jacketed with cotton wrapping. Curves were plotted of the 
temperature of the copper ball as a function of time and a tangent to 
these curves drawn at the point of room temperature enabled one to 



Fig. 1. 
Specific heat of pure ferro-nickels. 

determine the rate at which heat was being conducted along the rod to 
the copper ball. Three determinations, in general showing good agree- 
ment, were made for each specimen and the average results are given 



Fig. 2. 
Thermal conductivity of pure ferro-nickels. 

in the table and plotted in Fig. 2. The conductivities of pure iron and 
pure nickel are taken from measurements of Jager and Diesselhorst.^ 

The results are in substantial agreement with those of Honda (loc. cit.) 
for alloys annealed in the same way, save that this investigator finds the 

» Abh. d. phys.-tech. Reichsanstalt, 3. 269. 1900. 



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130 L. R, INGERSOLL AND OTHERS. [^SS! 

minimum conductivity at 30 per cent, nickel instead of 35 per cent, as 
in the present case. It may be remarked, however, that Honda's alloys 
were prepared from low carbon steel and ordinary commercial nickel, 
while those used here were composed of materials electrolytically purified. 

Thermoelectric Power.^-The- thermoelectric powers relative to pure 
copper were determined with a Leeds and Northrup potentiometer. 
The specimens of the alloy used in this case varied in length from 3.5 cm. 
to 5.8 cm. and were turned down until the diameter was only .12 cm. to 
.18 cm. The hot junction was placed in a glass tube through which 
steam passed, the cold junction being kept in a stirred bath of ice and 
water. The average difference between the temperatures at the ends 
of the rod under these conditions was found to be about 96° C. 

It was found that a further decrease in the diameter of the. rod in- 
creased the measured thermoelectric powers somewhat but the general 
form of the curve was not in any way affected. The results are given 
in the table and in Fig. 3. It may be remarked, however, that they are 



\ 
I 



rVTirUT l«iC<VI 



Fig. 3. 
Thermoelectric power (against copper) of pure ferro-nickels. 

perhaps not quite as trustworthy as the preceding series on specific heat 

and conductivity, inasmuch as the exact composition of the alloys was 

not as accurately known in all cases and there was some uncertainty as 

to how well the specimens had been annealed. 

The curve shows a marked minimum at 35 per cent. Ni. This is in 

agreement with the work of Haken^ who found, particularly for the 

binary alloys of bismuth, marked anomalies in the thermoelectric and 

electrical conductivity curves for compositions giving a maximum in the 

melting point curve. Eagan and Emmett^ observed a similar minimum 

1 Ann. d. phys. 3a. 291, 1910. 
« Univ. of Wis. Thesis, 1913. 



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No^a?^^''] PHYSICAL PROPERTIES OF NICKEL-IRON ALLOYS. I3I 

in the thermoelectric curve for bismuth-thallium alloys for a composition 
showing a maximum melting point. 

Electrical Resistance as a Function of Temperature, — ^This was deter- 
mined by the potentiometer method, a current of some 7.5 amperes 
being passed through the rod under investigation. A potentiometer of 
special type designed and built in this laboratory was used. The rods 
were heated in a nichrome wound furnace and the temperature measured 
with a copper-constantan thermocouple. The results are plotted in the 
curves of Fig. 4, while the specific resistance at 20° C. is included in the 



Fig. 4. 

Specific resistance at different temperatures of pure ferro-nickels. 

table, as well as the temperature coefficient for the range 0° to 100°. 
While it will be noted that the temperature coefficient for this range 
shows minima at 18 per cent, nickel as well as 35 per cent., it is evident 
from the curves of Fig. 4 that if a somewhat larger temperature range 
were taken the lowest point of the curve would be for the 35 per cent, 
alloy. The general form of these curves (aside from the minima at 26 
per cent. Ni) is in agreement with the resistance curve given by Burgess 
and Aston (loc. cit.) for ordinary temperatures. 

The thermal conductivity and electrical resistance measurements 
could be used to prove the law of Wiedemann and Franz that the thermal 
and electrical conductivities of a metal are proportional. A superficial 
examination of the table is enough to show that this is at least approxi- 



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132 L. R. INGERSOLL AND OTHERS. [ISSS 

mately true in this case, although a careful comparison is not possible 

since the two measurements were not carried out on exactly the same set 

of alloys. The law is very well proved for the nickel-steels, however, 

by Honda (loc. cit.). 

Conclusions, — The results of the present work show that the 35 per 

cent, nickel alloy, corresponding to the composition FejNi, has physical 

properties more or less markedly different from the other ferro-nickels. 

When the measurements of these various physical characteristics are 

plotted as a function of the composition the following general facts are 

brought out : the melting point curve* shows a maximum, specific heat a 

maximum, thermal conductivity a minimum, thermoelectric power a 

minimum, specific resistance a maximum and temperature coefficient of 

resistance a minimum — all at, or very near, the composition of 35 per 

cent, nickel. 

Physical Laboratory, 

University of Wisconsin, 
Feb. 5. 1920. 

1 Vide Guertler and Tatnmann, Zeitschrift fUr Anorg. Chem.. 24, 205. 



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Na*2.^^''] LINEAR RESONATORS. 1 33 



THE SELECTIVE REFLECTION OF HEAT WAVES BY 
LINEAR RESONATORS. 

By E. C. Wbnte. 

Synopsis. 

Vacuum-Uhermocouple. — The construction of a vacuum-thermocouple of high 
sensitivity and quick action for measuring heat radiation is described. 

Isolation of Long Heat Waves. — A method is given for isolating radiation of great 
purity and having a mean wave-length of 96 m- This radiation is obtained by 
combining a quartz lens focal isolation apparatus with reflecting surfaces of potassium 
iodide. 

The Reflection of Radiation by Linear Electric Resonators of Microscopic Dimen- 
sions. — Resonators were ruled from films of silver chemically deposited on glass 
plates. The reflecting power of such resonators was measured for the 96 m waves. 
Square resonators, the length of whose sides are small compared with the wave-length 
reflect little more than bare glass, provided the resonators are separated sufficiently 
to prevent conduction between adjacent edges. Resonators of equal width and 
separated by a distance of approximately one half of a wave-length were found 
to produce a maximum of reflection when their length was equal to 0.3 of the wave- 
length. The metal strips, although microscopic in size, thus show electrical 
resonance when stimulated by long heat waves. The results are in every way com- 
parable with those that have been obtained with the longer electric waves. 

OINCE the work of Hertz on electric waves a large number of experi- 
^ ments^ have been carried out on the transmission and reflection of 
such waves by groups of linear resonators.^ It has been found that a 
maximum amount of radiation is reflected from a plane surface over 
which such resonators are distributed in parallel rows and columns when 
the wave-length is from two to three times the resonator length, the 
exact value depending principally upon the position of the individual 
resonators relative to each other, and upon the dielectric constant of 
the material with which they are in contact. Only a few experiments of 
this nature have been undertaken with radiation of shorter wave-lengths 
such as is emitted from hot bodies, chiefly on account of the difficulty of 
making resonators of microscopic dimensions. The first experiments 

^A. Garbasso, Atti. Ace. di Torino, 28, 470 and 816 (1893), Garbasso and Aschkinass, 
Ann. d. Phys., 53, 534 (1894). Aschkinass and Schaefer, Ann. d. Phys., 5, 489 (1901). 
CI. Schaefer, Ann. d. Phys., 16, 106 (1905). Blake and Fountain, Phys. Rev., 23, 257 (1906). 
M. Paetzold, Ann. d. Phys., 19, 116 (1906). Woodman and Webb, Phys. Rev., 30, 561 (1910). 
Nelms and Severinghaus, Phys. Rev., i, 429 (1913). 

* The term linear resonator as here used may be defined as any metallic rod or rectangular 
piece of metal foil whose length is at least twice its greatest width. 



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134 ^- ^- WENTE. JSw! 

on reflection by groups of resonators in the field of infra-red spectrum 
were carried out by Rubens and Nichols^ in 1897 with plane polarized 
residual rays from fluorite, which had a mean wave-length of 23.7 m- 
Silver films, chemically deposited on glass, were ruled with a diamond on 
a dividing engine in such a way that the whole surface was left covered 
with regularly spaced, rectangular pieces of silver 5 fx wide and with 
separations of 5 fi. Four such surfaces were prepared, on each of which 
the resonators were of different lengths. When the residual rays were 
allowed to fall on these surfaces, it was found that a greater proportion 
of the incident radiation was reflected when the electric component was 
parallel than when it was perpendicular to the axis of the strips, and that 
in the former case the amount reflected was greatest when the resonators 
had a length approximately equal to an even multiple of a quarter of a 
wave-length. The results were hardly more than qualitative, however. 
Only four of a larger number of resonator plates that were ruled were 
deemed suitable for the experiments. On all the rejected plates 10 
per cent, or more of the resonators were torn away during the difficult 
process of ruling. The spacing between the resonators was insufficient 
to produce a very sharp maximum in the reflecting power regarded as a 
functipn of the resonator length. Although the radiation as obtained 
by reflection from fluorite plates had a maximum at 23.7 fi, it was not as 
homogeneous nor as completely polarized as was desirable for these 
experiments. 

In 1912* Wood performed experiments of a similar nature with the 
very long waves obtained from a Welsbach burner by the method of focal 
isolation. This investigator ruled the metal film of a "half-silvered" 
quartz plate into small squares. The film cut in this way was found to 
be entirely opaque to the long heat waves, although the linear dimensions 
of the squares were less than one tenth of a wave-length. Wood also 
performed some experiments with plates on which were deposited minute 
spherical metal particles, but found no indication of resonance.* Thus 
Wood failed to verify the results obtained by Rubens and Nichols. 

The experiments described below were undertaken for the purpose of 
making a more complete study of the reflection of heat waves by linear 
resonators, particular attention being given to the highly important 
consideration of having the resonators well spaced in order to make the 
resonance as sharp as possible. The radiation with which Rubens and 
Nichols carried out their experiments had a mean wave-length of only 
23.7 M. Methods are now available for isolating radiation of much 

1 Phys. Rev.. 5, 164 (1897), and also Ann. d. Phys.. 60, 418 (1897). 

* Phil. Mag., 25, 440 (1913). 

> Phil. Mag., 25, 440-443 (1913)- 



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Vol. XVI.l 
No. 2. J 



LINEAR RESONATORS. 



135 



r^ 



longer wave-length,^ so that the difficulty of making resonators of proper 
dimensions and spacings is considerably less. 

Construction of Vacuum Thermo-couple. 

In order to be able to rule metallic films into rectangles of the proper 
size it is advantageous to work with as long heat waves as possible. 
On the other hand, the amount of energy available decreases rapidly 
with the wave-length. For instance, in the case of the radiation ob- 
tained by Rubens and Wood by their quartz lens focal isolation method^ 
the deflection of the radio-micrometer, even when the radiation was un- 
polarized, was only about i cm. A measuring instrument of the highest 
sensitivity is therefore necessary. 

Of the various types of apparatus that have been used for radiometric 
measurements in the infra-red region, a vacuum thermo-couple with 
galvanometer seemed to be best adapted for use in this investigation. 
Recent experiments* have shown that the sensitivity of a thermo-couple, 
is increased from four to seven times 
when used in a high vacuum; at the 
same time convection currents, which 
may cause fluctuations in the read- 
ings, are eliminated. In a theoretical 
paper on the design of vacuum ther- 
mo-couples Johansen* has discussed 
the values that must obtain for the 
dimensions of the lead wires and the 
area of the receiving surfaces at the 
junctions of a vacuum thermo-couple 
for maximum sensitivity. The ther- 
mo-couple here described was de- 
signed so as to conform to these values as nearly as possible. 

The general arrangement of the thermo-couple finally constructed is 
shown in Fig. i. The leads are of bismuth and bismuth-tin alloy (Bi 
95 per cent.; Sn 5 per cent.). Bismuth wire, made by Heraeus, was 
kindly supplied to the writer by Prof. H. M. Randall, of the University 

> Rubens and Wood, Phil. Mag., 21. 249 (i9ii>. Rubens and Hollnagel, Sitzber. der 
Preuss. Akad.. Jan. 20, 191 o. 

• P. Lebedew, Ann. d. Phys., 9. 209 (1902). 

W. H. J. Moll, Arch. Neerland des Sc. Ex. et Nat. (II). 100. 

A. H. Pfund, Publ. Allegh. Obs., 3. p. 43 (1913); Pbys. Zeit., 15. 876 (1913). 

E. S. Johansen, Ann. d. Phys., 33, 517 (1910). 

Reinkober, Ann. d. Phys., 34, 348. 

W. Coblentz. Bull. Bur. of St.. 11. 621 (1915). 

* Loc. cit. 




S 



Fig. 1. 
Front view of thermo-couple. 



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136 E. C. WENTE. II5S^ 

of Michigan. The alloy was made from commercial bismuth and tin. 
A junction formed from these materials gave a thermo-electric power of 
135 microvolts per degree centigrade. The leads, a, are 2.5 mm. long 
and were all made of such a size that their resistance was 2.5 ohms each. 
In order to obtain leads of this size, small pieces of the material were 
pressed between glass plates and then cut into narrow strips with a razor 
blade. The resistance of each strip was measured separately, and those 
pieces not having the proper resistance were rejected. The ends of the 
leads were attached by a very small amount of solder of low melting 
point to the receivers, 6, which consist of sectors of silver foil of 0.0005 
cm. thickness and of 2 sq. mm. area. 

Although a junction formed from bismuth and bismuth-tin alloy gives 
a high thermo-electric power, these materials have not been used exten- 
sively because the thermo-couples become easily broken, the alloy par- 
ticularly being quite brittle. To avoid this difficulty the receivers were 
attached with a trace of shellac to the stretched quartz fibers, c, having a 
diameter of about 0.002 cm. The fibers are fastened to one end of a 
short piece of glass tubing, e. The heat conductivity of these fibers is 
quite negligible. The copper terminal leads, d, were attached by a 
glass seal to the other end of the glass tubing as shown in Fig. 2. A 
thermo-couple put together in this way will withstand a great deal of 
jarring without becoming broken. 

The receiving surfaces, instead of being blackened on the front side 
in the usual way, were coated with a thin layer of water glass to which 
had been added a small amount of India ink. While unblackened sur- 
faces are not good absorbers of ordinary light, Rubens and Wood* found 
water glass to be an especially good absorber of radiation of long wave- 
lengths, whereas lampblack is almost perfectly transparent to these 
waves. 

The thermo-couple was mounted in a glass container as shown in 
Fig. 2. The glass tube, e, on which the thermo-couple was mounted was 
placed inside of another glass tube, c, and attached to it with sealing wax 
in order to keep the receiving surfaces about a millimeter away from the 
quartz window, a. This quartz window, had a thickness of i mm. The 
vacuum was maintained by liquid air and charcoal. By means of a small 
discharge tube, attached as shown, the general state of the vacuum could 
be determined. 

One of the chief disadvantages of a thermo-couple for use in radiation 
measurements has generally been considered to be its sluggishness. In 
order that a thermo-couple may respond quickly to variations in the 

» Phi. Mag., 21, 249 (1911). 



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No'a'!^^''] LINEAR RESONATORS. I37 

intensity of the radiation, the leads should be short and the junctions 
should have a small heat capacity. In the case of the couple just 
described, because of the high conductivity of silver, it was possible to 
make the receivers of silver foil of very small thickness. Supporting all 
the parts of the couple on quartz fibers eliminates the usual long lead 
wires going to the supporting frame. 
Although the receiving surfaces of the couple were not entirely ** black** 



Fig. 2. 

Mounting of thermocouple in evacuated tube. 

for ordinary light, nevertheless, with the couple mounted as shown in 
Fig. 2, when connected to a galvanometer having a resistance of 25 
ohms and a sensitivity of i X io~*® amperes per mm., a deflection of 
2,500 mm. per candle meter was obtained. This sensitivity compares 
favorably with that of any instrument heretofore described, having the 
same receiving area. 

The Galvanometer. 

The galvanometer used with the thermo-couple was identical in design 
with that described by Nichols and Williams^ except for a slight modifica- 
tion of the shields. Instead of a cylinder of silicon steel, the intermediate 
shield consisted of 35 turns of 0.04 cm. transformer iron, wound spirally, 
the layers being separated from each other by paper 0.04 cm. thick. 
The efficacy of this type of shielding has been investigated both 
theoretically and experimentally by Esmarch.^ The three shields com- 
bined were found to have a shielding ratio of about 40,000. 

The zero position and sensitivity of moving magnet galvanometers 

1 Phys. Rev., 27, 250 (1908). 
* Ann. d. Phys., 39, 1550 (1912). 



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138 E, C. WENTE. [iJSS's': 

have generally been controlled by means of a special magnet provided 
for that purpose. This has usually been necessary in order to overcome 
a certain amount of residual magnetism either in the shields or in some 
of the other parts in the immediate neighborhood of the moving magnets. 
With this arrangement slight variations in the strength of the residual 
field will cause a drift of the zero position, which may impair the accuracy 
of the readings. In the instrument here described this residual magne- 
tism was reduced practically to zero by very carefully demagnetizing 
the inner shield and by winding the galvanometer field coils with non- 
magnetic copper wire. No control magnet was necessary, as the moving 
system followed almost exactly any angle through which the upper end 
of the quartz fiber suspension was turned. The quartz fiber was selected 
of a thickness to give the desired sensitivity, which in most of the work 
was 5 X lo""" amps, per mm., with the scale at a distance of one meter. 
With this sensitivity the galvanometer had a period of about 12 sec. for 
a complete oscillation. 

The galvanometer was supported by a Julius suspension, and to 
prevent disturbances from air currents and temperature changes the 
frame of the Julius suspension together with the galvanometer was sur- 
rounded by a box. Heavy copper leads were used to connect the thermo- 
couple to the galvanometer. Soldered connections were used throughout, 
and all junctions were protected as much as possible from circulating 
air currents. In spite of all these precautions, during certain hours of 
the day the galvanometer zero reading varied several millimeters; these 
fluctuations were apparently caused by earth currents as during other 
periods the zero reading was constant to a small fraction of a millimeter. 

Method of Isolating Radiation of Long Wave-length. 

In order to make satisfactory resonators on glass by ruling silvered 
surfaces, it is desirable to work with the longest wave-lengths possible. 
The method of focal isolation with a Welsbach burner as a source, 
according to the experiments of Rubens and Wood,^ gives radiation which 
is distributed over a fairly wide spectral region, but has quite a distinct 
maximum of energy at about 100 m wave-length. A modification of this 
method was adopted for this investigation. 

The general arrangement of the apparatus is shown in Fig. 3. a and 
a' are quartz lenses having a thickness of 0.7 cm. at the center and 
0.35 cm. at the edge, a diameter of 4.4 cm. and a focal length for ordinary 
light of 13.5 cm. c shows the position of the surface whose reflecting 
power is to be studied. The opening, and the reflecting surface at C 

» Loc. cit. 



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Vol. XVI.1 
No. a. J 



LINEAR RESONATORS, 



139 



have diameters of 0.5 and i.o cm. respectively. The lens a' is placed 
in a position such that the radiation of long wave-length is brought to 
a focus at c. Coming from c, it is reflected from plane surfaces at e and 
/ and then again brought to a focus on the central junctions, A, of the 
thermo-couple by the lens, a. The short waves, which would otherwise 
pass through the central parts of the lenses, are stopped by the metal 




■ ■ ■ ■ f , 



cm. 



^ 




Fig. 3. 

discs g and g' , The shutter, 5, is made of a plate of rock salt 3 mm. 
thick. Rock salt is almost perfectly transparent up to the point where 
quartz is a total absorber, and is opaque to radiation beyond 80 m» where 
the quartz begins to transmit freely. At h is placed a Fabry and Perot 
interferometer such as was first used by Rubens and Hollnagel^ for 
measurements of wave-lengths in the infra-red region. The plates are 
made of quartz 3 mm. thick the inner surfaces of which are plane to 
within a few wave-lengths of sodium light. 

At (/ is a polarizer which consists of a plane grating made of platinum 
wires 0.025 mm. in diameter separated by a distance of 0.025 n^"^- A 
grating of this type has been investigated by DuBois and Rubens,* who 
found that for long heat waves the transmitted radiation was almost 
completely polarized. The grating, which had a diameter of only i cm., 
was easily made by winding the wires on a metal frame and spacing them 

» Phil. Mag., 19, 761 (191 1). 

« Ber. der D. Phys. Gesell., 9, 431 (i9")- 



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I40 E, C. WENTE, ^wiS! 

by means of a guide fastened to the carriage of a dividing engine. The 
wires were then soldered to the frame and those on one side of the frame, 
removed. In this manner little difficulty was experienced in making 
sufficiently good gratings of the small size required. 

The apparatus as described above is very similar to that used by 
Rubens and Wood,^ who found that the radiation reaching the thermo- 
couple, when a Welsbach burner was used as a source, had a mean 
wave-length of approximately ioom» but the energy was distributed 
over a rather wide spectral region. For this investigation it is highly 
desirable that the radiation should be as nearly monochromatic as pos- 
sible. The radiation was therefore purified further by introducing 
reflecting surfaces of potassiums iodide at e and /. The residual rays 
from potassium iodide have a wave-length somewhat less than loo/n*. 
This value coincides very nearly with the mean wave-length of the 
radiation obtained by the focal isolation method with a Welsbach 
burner. 

These reflecting surfaces of potassium iodide were prepared by grinding 
the salt to a powder, and forcing it against a piece of heavy plate glass 
with a pressure of about 450 kilograms per square cm. When the pres- 
sure was relieved, the salt was left in a solid mass, which could easily 
be removed from the glass plate, the surface adjacent to the glass being 
left in a perfectly smooth condition, so that no grinding or polishing 
was required.' 

Fig. 4 shows an interferometer curve which was taken with the appa- 
ratus arranged as described but with silver instead of potassium iodide 
surfaces at e and /. The ordinates represent deflections of the gal- 
vanometer resulting from the opening of the shutter, s. The abscissae 
give the separation of the interferometer plates, except for an additive 
constant, as no special pains were taken to determine the exact distance 
between the plates for the smallest separation. 

If the energy distribution with respect to wave-length had but one 
maximum, the curve obtained in this way should have a form similar to 
that of a damped sine-wave, that is, the amplitudes of the periodic 
variations in the galvanometer deflections should decrease gradually 
with the separation of the interferometer plates. In the curve shown, 
these amplitudes first decrease and then increase and finally decrease 
gradually. This fact shows that the spectral distribution curve of the 
radiation has more than one maximum.* The radiation so obtained 

* Loc. cit. 

> Rubens and HoIInagel, loc. cit. 

* This method of preparing reflecting plates appears to have been used first by Miss G. 
Langford, Phys. Rev., 33, 137 (1911). 

* Rubens and HoIInagel. loc. cit. 



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Physical Review, Vol. XVI., Second Series. 
August, 1920. 



Plate I. 
To face page 140. 




Fig. 7. 




Fig. 9. 



E. C. WENTE. 



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Vol. XVI, 
No. 3. 



LINEAR RESONATORS. 



141 



is therefore quite unsuited for investigating the reflecting power of 
resonators. Rubens and Wood concluded from the curve obtained by 
them with apparatus of the same type that the spectral distribution 
curve had only one maximum; but apparently they did not continue 

















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their observations to sufliciently large separations of the interferometer 
plates to determine the real character of the energy distribution of the 
radiation. The fact that there are several maxima is probably due to 
absorption bands of water vapor.^ 

The curve of Fig. 5 corresponds to that shown in Fig. 4 except that the 

25r 




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zocT 
Fig. 5. 
> H. Rubens, Sitzber. der Preuss. Akad. der Wiss., 28, p. 513 (1913)- 



300 



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142 



E, C. WENTE. 



fSsCOND 

LSeribo. 



silver plates at e and / were replaced by the potassium iodide surfaces. 
This curve, being very similar to a damped sine-wave, indicates that the 
energy of the radiation reaching the thermo-couple is grouped principally 
about a single wave-length. This wave-length may be calculated from 
the distances the interferometer plates were moved between successive 
maxima or minima. The mean of all these distances is 47.9/* from 
which we determine the principal wave-length as 2 X 47.9 or 95.8 n. An 
approximate idea of the energy distribution curve in this case may be 
obtained, if, following the method adopted by Rubens and Hollnagel, 
we assume that this has the form of a resonance curve when plotted as 
a function of the wave-length, i.e., 

where Xo is the wave-length for which the energy of the radiation has a 
maximum value, #0, which in this case we assume to be 95.8 n. d is the 
logarithmic decrement, as obtained from the interferometer curve. 5,, 



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Fig. 6. 
Distribution of the energy of the radiation as a function of the wave-length. 

as determined from the curve of Fig. 5, assumed as a damped sine- wave, 
has an approximate value of 0.25. With these values of Xo and h #a» 
plotted as a function of X, gives the curve shown in Fig. 6. This curve 



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VouXVI.! 
Naa. J 



LINEAR RESONATORS. 



143 



shows that the greater part of the radiation lies within a narrow band of 
wave-lengths. 

All the preceding measurements were made with a Welsbach burner 
as source. A quartz mercury vapor lamp was tried but apparently 
gave less radiation of the desired wave-lengths even when operated at 
very high voltages. 

Construction of Resonators. 

In order to make resonators of the small size required for these experi- 
ments silver was chemically deposited on pieces of plate glass 0.4 cm. 
thick and the fresh deposit ruled into rectangles of the proper size with 
a diamond on a dividing engine. For this method to work satisfactorily 
the silver deposit should be uniform in thickness and adhere firmly to 
the glass. These conditions seemed to be best satisfied by the use of 
the formaldehyde silvering process.^ Best results were obtained only 
when the glass plates were first immersed in a hot solution of chromic 
acid. The silvering process was so regulated as to give coatings of prac- 
tically the same thickness for all of the plates. This thickness was such 
that the silvered surfaces reflected the 96 m radiation as completely as a 
plate of silver several millimeters thick, although they were not entirely 
opaque to light in the blue region of the visible spectrum. 

In order to obtain resonators that are widely separated it is necessary 
to remove the silver deposit in wide strips. If an attempt is made to 
make wide cuts with a diamond, a large proportion of the resonators 
will be carried away, whereas clean cuts result, if the diamond is set so as 
to rule a fine line by having one of its natural edges parallel to the direc- 
tion of the cut. To remove the silver in wide strips it was found most 



K 



-E 



i. 



Fig. 8. 

satisfactory therefore to rule fine lines but so close together that no 
metal remained between adjacent rulings. In this way it was possible 
to leave very narrow strips of silver and separated by as wide a space as 
desired. Light watch oil, flowed over the surface during the ruling, 
carried away the chips of silver removed by the diamond and so prevented 
* Wood, Physical Optics, p. 281, 1914 edition. 



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144 



£. C. WENTE. 



rsscoMD 
LSbkibs. 



their accumulation under the cutting edge. Fig. 7 is a photomicrograph 
of a part of a set of resonators ruled in this way. This particular photo- 
micrograph was taken of the plate listed as No. 7 in the table below. It 
shows the character of the resonators on all the plates numbered from 
I to 8. The following table gives the dimensions and spadngs of the 
resonators of all the plates that were used in this study. Fig. 8 will 
make clear the meanings of the terms used in the table. 

In the experiments of Wood^ on the reflection of long heat waves by 



No. of PUte. 


/(m). 


wCm). 


^lO*). 


^.(m). 


1 


13.0 

17.2 

21.35 

25.5 

29.7 

33.85 

38.0 

42.2 

15.0 

15.0 


R 


44 S 


4 


2 








1 

1 
1 
1 
1 
1 




3 




4 




5 




6 




7 




8 




9 


15.0 
150 


17.0 
270 


2 


10 


12 










•" 





ruled silvered surfaces it was found that single narrow cuts made by 
the diamond did not alter the resistance of the film appreciably. This 
result was verified. A single fine cut of the diamond increased the 
resistance of the film only slightly, although as far as could be determined 
from the image given by the microscope the silver had been removed 
completely. When several adjacent cuts were made so that the gap was 
2 or 3 /i wide the resistance was increased, but only after the total width 
of the space was roughly 5 n did the resistance become practically infinite. 
Apparently when the diamond makes a narrow single cut, the silver is 
not completely removed from the gap, although it does appear so when 
observed with a microscope. However, if the surface was ruled so as to 
leave widely spaced strips of metal 5 or 10 /* wide, a single cross cut made 
the resistance along the strips practically infinite. In this case the 
diamond undoubtedly removes the silver in its path completely. 

Experimental Results. 

Wood^ found that when a silvered surface was ruled into regularly 

spaced squares, the reflecting power of the surface was the same as before 

the rulings were made, even if the width of the squares was only a small 

fraction of the wave-length of the incident ray. As one would expect 

* Loc. cit. 

* Loc. cit. 



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Vol. XVI.I 
No. 2. J 



LINEAR RESONATORS, 



145 



such a surface to reflect scarcely more than the bare glass it was thought 
worth while to make a further test of this point. Two silvered surfaces 
were therefore ruled into squares 15/* wide. In the first of these the 
cuts were about 2 /* wide and the resistance across each cut was approxi- 
mately 100 ohms per cm.; in the second set the cuts were made wide 
enough to make the resistance between the squares practically infinite. 
A photomicrograph of this plate is shown in Fig. 9. When these plates 
were used in turn as reflectors at c (Fig. 5), the former was found to 
reflect 70 per cent, of the incident radiation, whereas the latter reflected 
only 30 per cent., the reflecting power of a plate of silver being assumed 
as 100 per cent. A glass surface without any metallic deposit reflected 
20 per cent. The surface with the wide cuts, before being cross-ruled, 
reflected only 34 per cent, of the radiation when the electric component 
of the incident waves was perpendicular to the strips, but 86 per cent, 
was reflected when it was parallel to the strips.^ From these data 
it appears that the negative result obtained by Wood was very probably 
due to the fact that the squares were not separated completely from 
each other. 

The ideal method of stuyding the selective reflection of waves by a 
group of linear resonators is to determine the reflecting power of such a 
group for monochromatic radiation of varied wave-length. However, 
this method is impracticable because of the difficulty of obtaining pure 
radiation of the different wave-lengths 50 
required. A method virtually equiva- 
lent to this is to keep the wave-length ^ 
of the radiation constant and to meas- 
ure the reflecting power of a number of 
groups of resonators of different dimen- 
sions, but in each of which the quanti- 
ties, w, /, di, d^ (Fig. 8), bear the same 
relation to each other. It is rather 
difficult to rule sets of resonators of ^^ 
different sizes with a fixed relation be- 
tween all the dimensions on account of 
the many different settings that have to 
be made on the dividing engine. How- 
ever, experiments on electric waves have shown that the quantities, dt 
and w (Fig. 8), affect the sharpness of resonance but little, provided / is 

* These particular measurements were made with the radiation obtained without the use 
of the KI reflecting surfaces. The radiation was therefore not as pure as is indicated by the 
curve in Fig. 6. 



30 



20 



r 



■/ 




ffEdPNATOfj u^mrwMj 



/o 



20 so 

Fig. 10. 



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146 E. C. WENTE. [U^ 

at least four times as great as w,^ The plates numbered from i to 8 in 
the table were therefore ruled so that all the dimensions except / were 
the same in each case. 

The percentage reflection of each of these plates was measured for the 
radiation obtained by the combination of the quartz lenses and potassium 
iodide reflecting surfaces (Fig. 3). These values, plotted as a function 
of the resonator length, i, are shown in Fig. 10. 

Concluding Remarks. 

The curve shown in Fig. 10 has a distinct maximum for a resonator 
length of about 29 fi. Although this maximum is not very sharp, it is 
sufficiently pronounced to show that the microscopic metal strips on the 
plates function as electrical resonators when stimulated by the heat 
waves 95.8 M in length emitted by a Welsbach burner. 

It may be of interest to compare the results here given with those 
obtained by other experimenters using electric waves and linear resonators 
made from tinfoil. Most of the work with electric waves was done with 
resonators in air. For this case the theoretical value* for the ratio of 
wave-length to the resonator length for resonance is given by some 
investigators as 2 and by others as 2.5. The ratio found by different 
experimenters varies between these values. Perhaps the most recent 
experimental investigation of this point is that of Nelms and Severing- 
hans,' who found that this ratio was a function of the axial separation of 
the resonators, but when the separation was greater than twice the 
resonator length, it approached the value 2.5. The curve shown in Fig. 
10 incidates that for resonance the wave-length (95.8 n) is 3.3 times the 
resonator length. Because of the high dielectric constant of glass the 
electrostatic capacity of the individual resonators is greater than is the 
case when they are completely surrounded by air, and for this reason it 
is to be expected that the ratio of wave-length to resonator length for 
resonance should be somewhat greater than 2.5. A similar result was 
found by Blake and Fountain^ for electric waves having a wave-length 
of 10 cm. and resonators made from strips of tinfoil. These investigators 
found that when resonators attached to a glass plate were separated 
axially a distance equal to 0.5 of a wave-length the ratio of resonator 

* Nelms and Severinghous, loc. cit. 

* MacDonald Electric Waves, p. m. 

M. Abraham, Ann. der Physik, 66, 435 (1898). 

Rayleigh, Phil. Mag., 8, 105 (1914). 

Oseen, Mat. Astron. Och Fysik (Stockholm), 9, 30, p. i (1914). 

* Loc. cit. 

* Loc. cit. 



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Na*a?^^'] LINEAR RESONATORS. 1 47 

length to wave-length for resonance was 3.5. It is not possible to make 
any accurate comparison between the values found for resonators on 
glass for electric waves and for the long heat waves used in the investiga- 
tion described in this paper; the dielectric constant, even if the same 
kind of glass were used, might be very different in the two cases because 
of the difference in frequency. The composition of the glass is un- 
doubtedly also an important factor. In spite of these different conditions 
the agreement between the value as found in this investigation and that 
given by Blake and Fountain for the ratio of wave-length to resonator 
length for resonance is very close. 

It would be very desirable to separate the amount of energy reflected 
by the resonators from the amount reflected by the glass. Rubens and 
Nichols^ assumed that the resonators and the glass reflected inde- 
pendently. It does not -appear that this assumption is altogether 
legitimate, as the experiments of Blake and Fountain show. They 
found that for certain resonator lengths less energy was reflected by a 
glass plate covered with resonators than from a plate of bare glass. 
There appeared to be no simple way of separating these two quantities 
so that the results are here given only for the composite structure. 

In the experiments of Rubens and Nichols it was found that a much 
larger percentage of the energy was reflected by linear resonators when 
the wave-length was equal to twice the resonator length. Not a sufficient 
number of resonators of different lengths were tried, however, to show 
the exact position of the maximum. The distance between the resonators 
which they used was a small fraction of a wave-length. Now, experi- 
ments* on electric waves have shown that as the separation between the 
resonators is decreased the length of the resonators for resonance is 
increased. For this reason it is probable that a resonator length equal 
to one half the wave-length was very nearly the proper length. It is 
therefore more than probable that the phenomenon observed by them 
was due to electrical resonance. The maximum reflection observed by 
Rubens and Nichols was 66 per cent, as compared with 35 per cent., 
the value found in the experiments here described; this difference is 
probably due to the fact that the number of resonators per unit area was 
much greater. The latter value agrees more closely with the value 
obtained by Blake and Fountain with electric waves. 

Although the results obtained in these experiments do not indicate 
that metallic resonators of the type considered reflect highly selectively, 
yet the reflection is so much greater within a certain region that the use 

* Loc. cit. 

* Blake and Fountain, loc. cit. 



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148 £. C. WENTE. ^ 



of such plates of resonators for isolating heat waves of a certain wave- 
length by multiple reflection does not seem altogether impracticable. 
Severinghans and Nelms^ used a similar method for obtaining electrical 
waves of much greater purity than was otherwise possible. Although the 
measurements of Rubens and Von Baeyer^ on the radiation obtained 
from a quartz mercury vapor lamp indicate the presence of wave-lengths 
as great as 600 Mi by far the larger proportion of the radiation was of 
much shorter wave-lengths. If this radiation were reflected a number 
of times from plates of resonators of proper dimensions the longer wave- 
lengths would be isolated more definitely. The outstanding difficulty 
in the use of such reflecting plates is that the energy finally obtained would 
be very small, perhaps too small, for accurate measurement with appa- 
ratus at present available 

In conclusion the writer wishes to acknowledge his indebtedness to 
Professor E. F. Nichols, who suggested the foregoing investigation, for 
his kindly encouragement and very helpful suggestions. 

Sloans Laboratory, 
Yale University. 
* Loc. cit. 
« Sitzber. der Berl. Akad., i, 666 (1911). 



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Naa?^^^] CRYSTAL STRUCTURE OP SODIUM NITRATE. 1 49 



THE CRYSTAL STRUCTURE OF SODIUM NITRATE. 

By Ralph W. G. Wyckoff. 

Synopsis. 

The crystal structure of sodium nitrate has been determined from a study of the 
Laue photographs obitained by passing X-rajrs through crystal sections. The 
method of interpretation is similar to that used by Nishikawa in studying spinel. 

The unit rhombohedron of sodium nitrate is a body-centered structure containing 
two molecules of NaNOs. The marshalling of the atoms in the crjrstal as a whole 
resembles that within a crystal of sodium chloride with NOs groups replacing the 
chloHne atoms of NaCl. 

MEASUREMENTS of the reflection spectra from the (100) and 
(in) faces of sodium nitrate have been made by W. L. Bragg.^ 
Because of the close crystallographic relationship between calcite and 
sodium nitrate and because of their similar spectra it was concluded that 
the atoms in sodium nitrate are arranged in the same fashion as are the 
atoms in the more thoroughly studied calcium carbonate. If this ar- 
rangement for the atoms in sodium nitrate is the correct one, then 
univalent sodium replaces divalent calcium, and tri- or quinquivalent 
nitrogen replaces quadrivalent carbon without changes in the crystal 
structure. The inevitable conclusion is that in these two compounds 
there is no peculiar connection between the valencies of the atoms con- 
cerned and their arrangement in space. 

This conclusion is of such great importance that it seemed desirable to 
assure its truth by a more detailed study of the structure of sodium 
nitrate. Consequently a determination of the crystal structure was 
made from a study of the Laue patterns obtained by passing rays through 
sections of sodium nitrate cut parallel to the (100) and the (in) faces. 
The method of interpretation is a modification of that used by Nishikawa* 
in studying spinel. 

The Specimens. 

The crystals used in these experiments were obtained by the slow 
evaporation over sulphuric acid of a solution of sodium nitrate. The 
specimens used were perfect rhombohedra about one centimeter on a side. 

* Bragg, W. L., Proc. Roy. Soc. (A), 8q, 468 (1914)- 

* Nishikawa, S., Tokyo Sugaku-Buturigakkwai Kizi (2), VIII., 199 (1915). 



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150 RALPH W, G. WYCKOFP, ^SS! 

Sodium nitrate crystallizes in the ditrigonal scalenohedral class of the 
hexagonal system. The crystallographic data are given as follows:^ 

a = 102'' 42.5'; a : c = I : 0.8297. 

The best determination places the density as 2.271.* 

The Lattice and the Number of Associated Molecules. 

A comparison X-ray spectrum of tungsten using NaCl (100) face, 
(a crystal of known spacing) and NaNOs, (100) face, was prepared. 
The equation for reflection is:* 

«X = 2d sin e. (i) 

X (the wave-length) for the various lines of tungsten is known ;^ sin B 
(where B is the angle of diffraction) can be determined by measurements 
upon the plate and from a knowledge of the distance from the crystal 
to the plate. The result of a number of closely agreeing values for djn 
(the ratio of the spacing to the order of the reflection) is 3.035 X 10"^ cm. 
The volume of a rhombohedral unit of structure of angle 102° 42.5' in 
terms of the spacing for the face (100) is 

V (the volume) = d'(ioo) X 1.077, 

mM 

V = = (PX 1.077, 

P 

where m = the number of molecules associated with the unit of structure, 
M = the weight of one molecule of sodium nitrate (85.01 X 1.64 X 10"^ 
gm.), and p = the density. 

(?/«» X 1.077 = w/«' X M/p, 

nVm = M/{d^/n^ X p X 1.077) (2) 

= 2.038 if the unit is a rhombohedron. 

It will be seen that the reflection closely corresponds with the second 

order spectrum from a rhombohedron containing four molecules of 

sodium nitrate. This is in agreement with the measurements of W. L. 

Bragg (op. cit.) and suggests a face centered arrangement similar to that 

deduced for calcite. Comparison of experiment with the other possible 

unit, the hexagonal prism, indicated that a structure having the hexagonal 

lattice is highly improbable. 

1 Groth, p.. Chemische Krystallographie. II.. 72. 
« Groth. P.. op. clt. 

* Bragg. W. H. and Bragg. W. L.. X-rays and Crystal Structure, Chap. 2. 

* Siegbahn. M.. Jahrb. d. Radioakt. u. Elektronik. XIII.. Heft 3. 296 (1916). 



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na"2.^^^i crystal structure of sodium nitrate, i5i 

The Location of the Atoms within the Unit of Structure. 

Several Laue photographs were made both with the rays at right angles 
to the (ill) face and also inclined at small angles to this normal 
position. One photograph was made with the rays perpendicular to 
the (100) face. The two symmetrical cases are shown in Figs, i and 2. 



Fig. 1 Fig. 2. 
Laue photograph obtained by passing Laue photograph obtained by pass- 
X-rays through a section of sodium ni- ing X-rays through a section of sodium 
trate in a direction normal to the (i 1 1) nitrate in a direction normal to the (100) 
plane. plane {original axes]. 

From a knowledge of the position of the crystal, the distance from the 
crystal to the photographic plate and the crystallographic data, the 
stereographic projection can in each case be prepared and the planes 
producing the various spots identified. When this is done using the 
commonly chosen angle between the axes (102° 42.5') there is no simple 
correspondence between spots and planes. If, however, the face diagon- 
als of the rhombohedron formed by taking the old axes as edges are chosen 
as axes, the observed spots prove to be due to simple planes. 

Calculations from Laue Photographs. 

Equation (i) connecting the spacing, angle of diffraction and wave- 
length of the X-rays holds true. The spacing d between like planes for 
a rhombohedral lattive is^ 



a\i + 2 cos^ tt — 3 cos^ a 

" V(A2 + jfe2 + /2) sin2 a + 2{hk + A/ + ife/)(cos2 a - cos a) ' 

where A, A, and / are the Miller indices of the plane, a is the angle between 
the rhombohedral axes and a is the length of the side of the unit rhombo- 
hedron. 



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152 



RALPH W, G. WYCKOFF. 



rSacoNs 
LSnttss. 



From equation (i) then 



«X = 



2a sin ^ Vi + 2 cos' a — ?3 cos^ ( 



(3) 



V(A2 + ife2 + /2) sin2 a + 2(Aife + A/ + ife/)(cos2 a - cos a) 

Sin B is readily obtained from measurements upon the photographic 
plate. The value of n\ calculated from equation (3) is plotted for the 
various spots estimated intensity of the spot. 

X-rays of a wave-length 0.44 — 0.47 X 10"^ cm. have a maximum 
effect upon the photographic plate. Consequently clustered about this 
first value of the wave-length, planes are found which are reflecting in the 
order, about twice this value of n\ planes reflecting in the second order, 
and so forth. In the tilted photographs corresponding planes will 
appear at different distances from the central spot and will be reflecting 
rays of different wave-lengths. If, in the prepared graph, these corre- 
sponding planes are connected, a set of curves of similar shape will be 
obtained, one above another and each representing the relative effect of 
different wave-lengths upon the photographic plate. If the atoms in the 





4 B 

Fig. 3. 
A\ is axis of crystallographic unit. a\ = 102® 42.5'. 

A\ is axis of the unit used in preparing the Stereographic Projections, aj •■ 
Ax\s axis of true unit. a% ■« 47** 14'. 



' 77* 24'. 



crystal are in the simple cubic array of a Bravais point lattice, the curves 
for planes with smaller spacing appear above those having larger spacing. 
Departures from these ideal conditions will be shown by planes of small 
spacing, giving more intense reflections (for a particular wave-length of 
X-rays) than the simpler planes. The non-appearance of a reflection 
from a plane placed in a favorable position for reflection is as important 
as the observation of a reflection. Many times the connecting of similar 
points by a curve is inconvenient. This is quite unnecessary as long as 



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Vol. XVI.l 
No. 2. J 



CRYSTAL STRUCTURE OF SODIUM NITRATE, 



153 



comparison is limited to only those points which are produced by waves 
of the same length. 

When such a plot is constructed using the indices of planes obtained 
from the second set of axes (angle = 77"^ 24'), it is found that a number 
of points, all having odd indices, appear to reflect strongly in the neighbor- 
hood of 0.24 X 10"® cm. This abnormality, however, could be removed 
by the choice of a third set of axes which are the diagonals of the faces 
of the unit rhombohedron made by the second set and are the true axes 
of the unit of structure of sodium nitrate. The relation between the 

































•rtt 




















•<T0 










•iti 


















































































































































^ 


m 


a& 


»*•* 


ii» 














\ 


*• 




ZO^• 






a 


2 


T! 


4 


iK . 


& 


6 


a 


B 



Fig. 4. 

The points which appear in this figure were chosen not because of their special importance 
but for the purposes of illustration only. 

three sets of axes is shown in Fig. 3. The graph for certain points of the 
first unsymmetrical (tilted) photograph (indices those of the third set 
of axes) is given in Fig. 4. 

The Arrangement of the Atoms. 

The symmetry of sodium nitrate is that of the point group D^^, The 
spectrum measurements and the inspection of Laue photographs indicate 
that the fundamental lattice is rhombohedral. There are two space 
groups^ of Dz^ which have Trh as the fundamental lattice: DzJ" and Z>m*. 
The group in this case was found to be Z^s/. For Dzd^ the positions of 

* Sch6nflies, A., Krystallsysteme u. Krystallstruktur. 



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154 RALPH W, G. WYCKOFF, ^ 



COND 
•BRXKS. 



equivalent points are: 

(i) xyz, yzx, zxy; y22, zyx, £2y] 

(2) Tx — X, Ty — y, Tm — z; Tx — y, Ty — z, Tg — x; Tx — z, Ty — x,Tm — y\, 
Tx + yfTy + X, r, + s; r, + z, Ty + y, r, + x; r, + x, Ty + 0, r, + y; 

where the axes XYZ are taken along the newest crystallographic axes 
and Tg = Ty — r, (in length) is a translation of half the length of an 
edge of the unit cell in the direction of the subscripted axis. Two mole- 
cules of sodium nitrate must be placed within this unit cell of D^^ by 
the following choice of coordinates. 

N = 000 and a/2, a/2, a/2 where a = the side of the rhomb. 

Na = a/4, a/4, a/4; 3a/4, 3a/4, 3a/4. 

= /3, a - /3, o; o, /3, a - /3; a - /3, o, /3; a/2 - /3, /3 - a/2, a/2; 
/3 - a/2, a/2, a/2 - /3; a/2, a/2 - /3, /3 - a/2, 

where P/a is fractional part of a. 

For this arrangement of atoms the formula giving a quantity propor- 
tional to the intensity of the nth order reflection from a plane (hkl) will be 

A^ + B^oz Intensity (4) 

il = (i + cos rnrs) I i\r + iVa f cos «( - ) ) ^ + cos 2imfi(h — k) 

+ cos* mPil - A) + cos 2imfi(k -I) \\. 

B = (i — cos mrs)0 [sin 2Tnfi(h — k)+ sin 27r«iS(/ — A) + sin 2Tn/3(* — /)], 

where iV, iVa and O represent the diffracting (scattering) powers of 
nitrogen, sodium and oxygen respectively and s = h + k + I, 

Because of the uncertainty of the effect of spacing upon the intensity 
of reflection^ only spots from planes of nearly equal spacing which were 
undoubtedly reflecting in the first order were used in comparisons of 
intensity. 

The results of the study of the Laue photographs were used 

I. To test the truth of the general arrangement as outlined above. 

II. To obtain the probable value of /3. 

III. To compare the calculated data with the observed when this 
probable value of fi is used and to search for discrepancies which could 
be applied to the more accurate placing of oxygen. 

When n = I two cases of expression (4) arise according to the value 
o{s(h + k + /). 

» Bragg, W. H.. and Bragg, W. L., op. cit.. Chap. XI. 



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Vot.XVI1 
No. a. J 



CRYSTAL STRUCTURE OF SODIUM NITRATE, 



155 



Case I. — ^When s is odd (the indices are either all odd, or two even 
and one odd). 

i4 = o, 

B = 20[sin 2Trfi{h - Jfe) + sin 2t/3(/ - A) + sin 2Tfi(k - /)]. (5) 

Case 2. — ^When s is even (the indices are two odd and one even). 

i4 = 2 TiV + iVa cos (^ j 5 + 5 j cos 2t/?(A - *) 

+ cos 2t/3(/ - A) + cos 2ir/3(* - I . 
3=0. 

I. In Case i only oxygen atoms would be expected to reflect. If two 
of the indices are equal to each other (as in 335, 252) this B term also 
becomes zero. This is true no matter what value is assigned to j9 so that 
the presence or absence of such points gives one excellent means of testing 
the truth of the general arrangement of atoms'. No points of case i 
having two equal indices were found. 

II. Points of case i, except those where two indices are equal, can be 
used to place the oxygen atoms with accuracy. This can be done by 
plotting the variations in the value of the calculated amplitude with 
changes in the value of 0. The various points of case i which appear 
in the photographs group themselves according to the values of A — A, 
I — h, k — I, In Fig. 5 curves i, 2, 3, or 4 are due to groups of spots 







^'■ 


\ 






r 


\ 








/ 




\ 






1 


> 


•■■-. 




\\^ 


/ 




4 




/ 


/ 


A 




\ 


V 


5< 


n'- 


N, 


\ 


I 


/ 




^ 


f 


-2 




\ 




V, 


/ 






/ 


r 




1 




1 




^ 1 


J 


t 


4 


4 

ftS 



Fig. 5. 

whose values for A — k,l — h, and A — /are (— i, — 2,3), (— i, — 1,2), 
(2, 3, 5), and (7, 2, 5). These curves agree in all being intense only close 
to the point j9 = 1/4. The oxygen atom must lie, therefore, on the line 



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156 RALPH W. G. WYCKOFF, ^2S 

joining nitrogen atoms at a position near to one fourth of the distance 
from one nitrogen atom to the next. 

III. If the value of jS is exactly one fourth, planes fulfilling the condi- 
tion of Case I (5 is odd) fall into three classes. 

(a) When all the indices are odd, the B term of expression (5) becomes 
zero. 

(b) When the indices are two of them even and one of them odd and 
the difference between the even indices is divisible by 4^ the B term of 
(5) becomes zero. 

(c) When the indices are two of them even and one of them odd and 
the difference between the even indices is not divisible by 4, the B term 
of (5) is not zero. 

An examination of three Laue photographs which averaged reflections 
from one hundred and fifty planes each, failed to show a single plane of 
either class (a) or of class (b). This leads to the conclusion that the 
oxygen atoms deviate very slightly, if at all, from the position fi = 1/4. 

As would be expected, since reflection is not then restricted to the 
oxygen atoms, spots from planes having two odd and one even indices 
(Case 2) are most numerous and intense. These planes also are of two 
sorts. If, on the one hand, s is divisible by 4, the effect due to the sodium 
atoms adds to that due to the nitrogen and oxygen atoms in building up 
the reflection from a plane; but if s can not be divided by 4 the amplitude 
contributed by the nitrogen atoms is to be subtracted from the effects 
of the other atoms. For the same wave-lengths of X-rays and equal 
spacing of like planes, a plane of the first sort should reflect more strongly 
than one of the second. This was found to be true for those planes which 
gave spots upon the photographs. 

Conclusion. 

The results of these experiments confirm the structure as deduced 
by W. L. Bragg.^ Each sodium atom has arranged about it three equi- 
distant oxygen atoms. Each of the NOs groups thus formed is sur- 
rounded by six equidistant sodium atoms. Each sodium atom has the 
centers of six NOa groups equally far from it. This structure may thus 
be thought of as similar to sodium chloride with NO3 groups replacing 
the chlorine atoms. 

The arrangement of the atoms within the true unit of structure is 
shown in Fig. 6. The coordinates of the atoms within this unit cell are 
(assuming the length of the side as i) : 

N at (o, o, o) and at (K, M. K), 

» Bragg, W. L., op. cit. 



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Vol. XVI.l 
No. 3. J 



CRYSTAL STRUCTURE OF SODIUM NITRATE, 



157 



N at (X, X, X) and (^, K. ^^), 

at 03, I - iS, o); (o, fi, i - fi); (i - iS, o, fi); 

where jS has a value that is very close to }i. The length of the side of 




Fig. 6. 
The unit rhombohedron of sodium nitrate. 

this unit rhombohedron is 6.06* X 10"® cm. and the angle between the 

axes is 47** 14'. 

The writer wishes to express his thanks to the Department of Physics 

for the use of the apparatus necessary for carrying out these experiments. 

He is under deep obligation to Dr. S. Nishikawa without whose constant 

and kindly aid and criticism this work could not have been carried out. 

Department op Chemistry, 
Cornell University. 



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158 OTTO STUB LM AN, JR, ^^SSS, 



A NOTE ON THE CORRECTION OF CONTACT DIFFERENCE 
OF POTENTIAL DEVELOPED IN COMPTON'S MODI- 
FICATION OF THE QUADRANT ELECTROMETER. 

By Otto Stuhlman, Jr. 

Synopsis. 
A method of eliminating contact differenu of potential in Compton's modification 
of the quadrant electrometer is suggested. The quadrants must not be built up. 
Solder, fillers or finishers must be omitted. If the needle is of aluminium the 
quadrants must be of aluminium, milled out of a single piece of metal. The final 
curve shows the absence of contact difference of potential in such an instrument when 
reconstructed and possessing an aluminium needle and milled aluminium quadrants. 

TN an article on ''A Sensitive Modification of the Quadrant Elec- 
•*- trometer'*^ it is said that '*the most serious sources of difficulty 
appear to be irregularities in the needle, or quadrants, and contact 
difference of potential between the quadrants," and further that this 
effect is proportional to the first power of the needle potential. Inci- 
dentally it is also stated that **such contact differences of potential, if 
found troublesome, may be removed by cleaning (the quadrants) or 
compensated by a small potential permanently applied to the * earthed' 
quadrants." 

Unfortunately however, many conditions may arise when it is neither 
possible or desirable to have a compensating potential permanently 
applied to the *' earthed " quadrants. In these circumstances the contact 
difference of potential existing in the quadrant system of the instrument 
must be removed by structural changes. The simplest and most obvious 
changes would be to make all the quadrants as well as the needle of 
the same metal. The quadrants should not be made of several pieces 
soldered together as in the "Compton Electrometer," but should be 
cut from the solid metal and then machined to the proper size and shape. 

In Fig. I, are shown three examples to indicate how, under electro- 
static positive control, the scale deflections vary as the potential across 
the quadrants is increased. The scale deflections, proportional to B, 
are plotted in Figs, i, 2 and 3 so that, as in Fig. i for example, if the 
large deflections are to be strictly interpreted they must be read 
tan 2B = dlD, where d is the deflection and D the distance of the scale 

> A. H. Compton and K. T. Compton. Phys. Rev., Vol. 14. Aug., 1919. _ 



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Vol. XVI.l 
No. 2. J 



CONTACT DIFFERENCE OF POTENTIAL. 



159 



from the mirror. For the large deflections this correction is about one 
per cent. The potentials were measured by means of a standardized 
Simens and Halske millivoltmeter. The needle of the instrument was 
of aluminium foil and the quadrants of brass. Each of the latter were 
made of three pieces, top and bottom soldered to a circular vertical band. 




tl « U V 100 ito 

5cale DeVlectione m m.m. 

Fig. 1. 

If now the needle is kept at a definite potential and the deflections 
observed as the potential on the quadrants are increased, it is found that 
the curve would not pass through the origin. Changes in the potential 
of the needle say from forty to twenty and finally to ten volts developed 
curves which possessed approximately equal intercepts on the voltage 



o0O42 












^ 


^ 


:5 

5 








^^ 


^ 


^ 


4 

oOOM 






^ 


<^ 




-^ — 




3 




^ 


^ 






^ 


V40 


H00ft4 




yyy^ 


''^ ^ 


'''""^ 








^00 SO 


f 


€^ 


^ 























40 10 

DeUsction in m.m. 

Fig. 2. 

axis. This value was found to be 0.00292 volts. The quadrants were 
next adjusted to produce negative electrostatic control and the above 
observations repeated. The intercept of these curves had the same value 
as that of the above curve. 



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i6o 



OTTO STUHLMAN, JR. 



ISboomd 

LSERIBt. 



The quadrants were then removed, thoroughly cleaned in acid and 
scraped to remove all visible indications of solder. The observations 
were repeated and the voltage intercept was found to have dropped to 
0.00264 volts. In Fig. 2 is shown a typical set of results obtained under 
these conditions. They represent the quadrants adjusted to negative 
electrostatic control with 40 volts on the needle. The successive curves 
show that the intercept is independent of the degree of negative control. 
The upper curves were obtained under less electrostatic control than 
each of the successive lower ones. 

Hence variation in the degree of electrostatic control or potential on 
the needle does not change the value of the voltage intercept. 

Further cleaning and scraping of the quadrants did not reduce this 
value below 0.00170 volts. A tilt of the needle about its minor axis 
may account for the fact that the curves do not pass through the origin. 



M20 






1^ 




\f'tO 


.••IS 




,^ 


..-"' 










^^ 


^ 










^ 












i 






4 


^ 


< 


10 


•^ .M80 












V : 


a 

s 
I 

«00t0 




^ 








0010 


/ 


/ 










JD«0« 


/ 













5 >0 IS 20 t& 30 

De{-|ection u\ mm 
Fig. 3. 

This explanation was eliminated because the same needle without varia- 
tion in its tilt was used throughout the observations. A contact differ- 
ence of potential in the system would account for it, especially in view 
of the successive changes in the value of the intercept, as the physical 
conditions of the inner surfaces of the quadrants were changed. In 
order to test this hypothesis, the quadrants were replaced by aluminium 
ones constructed as suggested above, the aluminium foil needle retaining 
its original tilt. This structural change produced the results shown in 
the upper curve of Fig. 3. The supposed contact difference of poten- 
tial has been reduced to 0.00070 volts. An examination after twenty- 



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Naa^^^*] CONTACT DIFFERENCE OF POTENTIAL. l6l 

four hours and all later examinations showed no contact difference of 
potential and a typical curve developed under these conditions and 
under negative electrostatic control is shown in the lower half of Fig. 3. 
The curve passes through the origin. The subsequent drop from 0.00070 
to zero volts is of course accounted for by the occlusion of air on the new 
surfaces of the aluminium quadrants, ageing^ them to the same surface 
conditions as existed on the very much older aluminium foil needle. . 

A further point of interest in the above curves is the lack of uniformity 
in the sensitiveness for all values of the needle deflection. This has been 
pointed out by Compton, in that *'the presence of the term k^V^S^ in 
equation (5) shows that the sensitiveness is not the same for all values 
of $y i.e., over all parts of the scale, though this term is' not important, 
except at very high sensitiveness." Unfortunately no curves for this 
variation are shown in the above paper so that no comparison is possible. 
How close these curves approach to a straight line can be seen in the 
figures here presented. The best results were those obtained in Fig. i, 
when the needle was charged to 40 volts and the quadrants adjusted to 
electrostatic positive, though nearly zero, control. 

The data for this note was obtained while the writer was a member of 
the staff of the State University of Iowa. 
West Virginia U>avERSiTY, 

MORGANTOWN, W. Va. 

*See "On the Influence Contributing to the Variation of Contact Electromotive Force 
with Time," O. Stuhlman, Phys. Rev., Vol. 8, p. 294, 1916. 



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1 62 G, A. SCHOTT. ^SS 



NOTE ON THE ELECTROMAGNETIC FORCE BETWEEN 

TWO ATOMS. 

By G. a. Schott. 

Synopsis. 

Making use of results obtained in a previous paper giving the average radial 
repulsion exerted by a charge « on a charge e' when both charges are revolving in 
circular orbits at a great distance, the author obtains a formula for the force between 
atoms. He concludes, in reply to a criticism by A. C. Crehore, — 

In a passive neutral atom the radial force vanishes completely. 

When both atoms are ionited there is a residual force, negligible in comparison with 
an electrostatic force which may be taken to represent the chemical force between 
the ions. 

When one atom is neutral 4ind the other ionited, the electrostatic force vanishes, 
leaving a residual force, which is estimated to be too small to play anything but a 
very small part in chemical actions. 

I. Crehore 's preliminary reply* to my criticism* of his first paper* has 
just come to my notice. Previously I purposely confined my attention 
as far as possible to the supposed gravitational attraction between two 
revolving electrons^ but now Crehore has raised the question of the force 
between neutral atoms, so I will consider it briefly. 

The problem is to calculate the average radial force, to the order of 
the inverse square of the distance, exerted by an atom of type 2 on an 
atom of type i, both being supposed symmetrical about an axis, and the 
axes distributed uniformly in all directions on the average for a large 
number of atoms. My formula (50), p. 37, gives the average radial 
repulsion, F, exerted by a charge e, revolving in a circle with jS times the 
speed of light, on another charge e' at a great distance r in the form 

The formula (54), p. 456 of Crehore's earlier paper, when averaged for 
all directions of the axes of the orbits, is of the same form, but 

m = - i^. (2) 

The speed of the second charge e' does not occur at all, so that the law 

of action and reaction is violated, as Crehore objects. But this violation 

» A. C. Crehore, Phvs. Rev., Vol. XIII., p. 89. 
« G. A. Schott, Phvs. Rev., Vol. XII., p. 23. 
> A. C. Crehore, Phvs. Rev., Vol. IX.. p. 445- 



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No!"2?^^'l ELECTROMAGNETIC FORCE BETWEEN TWO ATOMS, 1 63 

follows directly from the use of retarded potentials, which express the 
fact that electromagnetic force, momentum and energy require time for 
their propagation. Without it we could not even account for electro- 
magnetic mass, which is a result of the unbalanced internal electromag- 
netic forces between the parts of the electron. 

2. In applying (i) to the problem of the atoms we replace e, jS, e' by 
— ex, P2t — eu or by £1, 0, £1, according as we seek the actions between 
the electrons, or the positive nuclei, of the atoms. The average radial 
repulsion is the sum of these four terms : 



(a) Electrons 2 acting on electrons i: 2tfi2ej{i +/092)}r~*, 

(b) Electrons 2 acting on nucleus i: — E{Ze2\i +f(fi2)\r' 

(c) Nucleus 2 acting on electrons i : — 2tfi£2^~^ 

(d) Nucleus 2 acting on nucleus i : EiE2f~^, 

Hence we find 



(3) 



F = {(2^1 - £,)(2ej - E2) + (2^1 - £i)2tf2/(iS2)}r-*, (4) 

where the summations are for all the electrons of the two atoms. The 
first term represents the electrostatic repulsion, the second a com- 
paratively small residual force, which for low speeds is of the order 
jSj' with (2), but only of order 02* with (i). There are three cases: 

(i) Passive atom neutral; 2ei = Ei. 

The radial force F vanishes altogether. 

In my opinion this disproves Crehore's objection to (i). He himself 
obtains a different result, because he retains the term/CjSa) in (3a), but 
omits it in (36) ; in other words he treats a passive nucleus differently 
from a passive electron, although the velocity of neither one nor the 
other occurs in (i) or (2). I cannot see any reason for this different 
treatment of passive negative and positive charges. It is different with 
Crehore's modified formula, which differs from (2) by the presence of an 
additional factor, viz., the Square of fi for the passive charge multiplied 
by a positive constant, chosen so as to account for ordinary gravitational 
attraction. Since (2) ought to be replaced by (i), the chief reason for 
this change disappears; besides, as it makes the formula agree with the 
law of action and reaction, it is difficult to reconcile it with the explana- 
tion of electromagnetic mass. 

(2) Both atoms ionized; 2ei + £1, 2^2 + £2. 

The residual force may*be neglected in comparison with the electro- 
static force, which may be taken to represent the chemical force between 
the ions according to the usual interpretation. 

(3) Active atom netitraly passive atom ionized; 2^1 + £i, 2^2 = £2. 



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1 64 G. A, SCHOTT. ^SS 

The electrostatic force vanishes, and we are left with the residual force 

F = (2^1 - £i)£^(iS2)r-*. 

Since /(iS2) is essentially positive according to (i), this force is a repulsion, 
or an attraction, according as the passive ion is negative, or positive. 
Taking ^2 to be of the order o.oi we see that the force is only of the order 
of one hundred-millionth of ordinary chemical forces. Thus it is not 
likely to play anything but a very small part in chemical actions, though 
it might conceivably be influential in solution phenomena and others 
of like nature. I think that I was quite justified in my former paper 
in expressing a doubt as to the possibility of detecting its existence by 
experiment. 



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Second Series. September, 1920. Vol. XVI., No. 3 



THE 

PHYSICAL REVIEW. 



CHARCOAL ACTIVATION. 

By H. Horton Sheldon. 

Synopsis. 

Adsorplwn*of Gases by Charcoal — Heal Effect. — The first part of this paper com- 
prises a study of the heat effect on the adsorption of hydrogen and nitrogen by 
charcoal, and is a continuation of the work of Dr. Harvey B. Lemon^ in which air was 
used. The charcoal is heated for periods varying from one hour to twenty hours at 
temperatures from 400® C. to 1000® C, and at the same time the gases given off are 
pumped out with a mercury condensation pump. The activity of the charcoal is 
tested after each treatment by its adsorption of gas at liquid air temperature, and 
the results are shown by curves where logarithm of time in minutes, is plotted 
against logarithm of pressure in centimeters. The agreement with predictions from 
the hydrocarbon theory of adsorption are pointed out. That activation takes place 
by slow oxidation at room temperature is also shown. 

A New Form of Charcoal — Selective Adsorption. — By heating to 1000** C. for 3J4 
hours, a sample of charcoal was put into a condition such that it adsorbed hydrogen 
more readily than nitrogen. Theory is advanced to account for this. 

THE results obtained at Ryerson Laboratory some time ago by Dr. 
Harvey B. Lemon^ on the activation of charcoal, and published 
recently, led at the time to two obvious suggestions; the first, that the 
activation was due to the oxidation from the air used — the hydrocarbon 
hypothesis; the second, that it was due to a modification of the charcoal 
structure, brought about by the heat treatment. 

Of these two, the hydrocarbon hypothesis met with the greater favor, 
and in articles published since the war* has been enlarged into a more 
or less complete theory. The observations on which, this theory was 
based, however, were apparently made from experiments in which the 
charcoal was tested under field conditions, such as existed in gas masks, 
and no attempt was made to free the charcoal from air, moisture, etc. 
Further, since no data was published in support of this theory, it was 
decided to perform some experiments here with pure gases to satisfy 

> Physical Review, Vol. 14, No. 4. Oct., 1919- 

* J. of Ind. and Eng. Chem., Vol. II., No. 5. May, 1919. N. K. Chaney, paper presented 
at Thirty-sixth General Meeting of the American Electro-Chemical Soc., Chicago. 1919- 

165 



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1 66 H. HORTON SHELDON. [iS^ 

ourselves of the conclusions drawn. Accordingly work was begun on 
pure nitrogen and pure hydrogen. 

In the course of the work, which was similar to that done by Dr. Lemon 
with air, it was observed that charcoal could be activated or deactivated 
so far as the adsorption of nitrogen was concerned, much more easily 
than was the case with hydrogen. This at once suggested the possibility 
of putting charcoal into such a condition that it would adsorb relatively 
a large quantity of hydrogen compared to nitrogen, thus being the reverse 
of all previously known charcoals. 

This was successfully carried out as noted in Science for December 19, 
191 9; and in a paper by the author before the American Physical 
Society in November, in which the method was described. So little 
has as yet been done on this, that it is at present impossible to predict 
its utility in commerce. 

The apparatus which was identical with Dr. Lemon's, consisted of a 
central volume, connected on the one side to a McLeod gauge and on 
the other to a mercury condensation pump. From the central volume 
branched three tubes which contained the charcoal, and each of which 
could be closed from the rest of the system by stopcocks. The tubes 
were made of iron and were connected to the glass system by ground 
joints. The gas in these tubes could be tested by the use of Geissler 
tubes attached to their sides, which were also used to roughly gauge the 
vacuum. The purity of the hydrogen used was tested by using the 
Geissler tubes with a disruptive discharge, but in the case of the nitrogen 
the test was made by observing the afterglow in an electrodeless discharge 
tube. 

Each charcoal tube contained 25.7 gms. of charcoal, which was dried 
by heating and weighed while still hot. The first tube contained U. S. 
Government 600-minute charcoal, and the other two Sample No. 16, 
which was carbonized at 670° C. for three hours. This latter was part 
of the same sample No. 16 used by Dr. Lemon and later by Dr. Lemon 
and Miss Blodgett.^ Only one of these latter tubes will be recorded, 
the second being used as a check only. 

The method used was to enclose the three tubes in a furnace and to 
heat the charcoal to various temperatures, and for various lengths of time 
as specified throughout the paper. All gases given off from the charcoal 
when heated, were pumped out by the condensation pump which was 
kept running, until, when the furnace was allowed to cool; it was closed 
off by a stopcock, at about 400° C. Below this temperature an auxiliary 

» Physical Review, Vol. XIV., No. 5. Nov., 1919. 



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Na*3^^^*] CHARCOAL ACTIVATION. I67 

charcoal bulb immersed in liquid air was used to insure a good vacuum. 
This process has been called ''outgassing.** 

The central volume was then filled with the gas whose adsorption it 
was desired to measure, and readings taken on the individual charcoal 
tubes at liquid air temperature. 

These readings are shown on the graphs where the logarithm of the 
time in minutes is plotted against the logarithm of the pressure in centi- 
meters. With the exception of the curves in Figs. 5 and 6, which were 
taken with an initial volume of 1,780 c.c. (at normal temperature and 
pressure) all the curves were taken with an initial volume of 926 c.c. 

normal. 

Part I. 

The curves of Fig. i are the adsorption curves of hydrogen. Curve i 
was taken after a preliminary outgassing of 15 hrs. at 400° C; curve 2 
after 8 hrs. at 400° C. ; and curve 3 after 20 hrs. at 400° C. 



Fig. 1. 

It will be observed here that the final pressure is unchanged throughout, 
while at this temperature when air was used the charcoal was greatly 
activated. This agrees with the hydrocarbon theory that the activation 
at this temperature is due to the removal of inactive hydrocarbons by 
oxidation. The fact, however, that the rate of adsorption is greatly 
increased as shown by the drop in the initial end of the curve may be 
of significance and is discussed later. 

In Fig. 2, curve i is curve 3 re-drawn from Fig. i. Curve 2 was 
taken after 16 hrs. at 600° C; curve 3 after 15 hrs. at 700° C; curve 4 
after a second 15 hrs. at 700° C; curve 5 after 10 hrs. at 800° C. and 
curve 6 after 9 hrs. at 800° C. 

From the figure it will be seen that an outgassing at 600° C. had no 



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1 68 H. HORTON SHELDON. [sLun. 

effect, and so from this it may be concluded that any temperature below 
this is incapable of driving off hydrocarbons when only hydrogen is 
present. The first outgassing at 700° C. gives a decided improvement, 
showing that, according to the hydrocarbon theory, the boiling point 
of some of the hydrocarbons had been exceeded. The activity attained 



l.O 
..LOO. TIIOU. 



Fig. 2. 

after 15 hrs. of this temperature was not improved after a second run of 
15 hrs. Apparently all the hydrocarbons that could be driven off at this 
temperature were driven off in the first outgassing. 

Ten hours at 800° C, however, again gave improvement, showing 



Fig. 3. 

that other hydrocarbons had been driven off. A second 9 hours showed 
that no further improvement could be made at this temperature. Thus 
this set of curves shows three slightly different stages of activity. 

In Fig. 3, curve i is curve 6 of Fig. 2 re-drawn. Curve 2 is taken 
after 5 hrs. at 900° C; curve 3 after a second 5 hrs. at 900° C; and 
curve 4 after 10 hrs. at this same temperature. 



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Na'i!^^*] CHARCOAL ACTIVATION. 1 69 

In the case of Sample 16, we find a slight activation after the first 
outgassing due no doubt to hydrocarbon removal, while subsequent out- 
gassings deactivate. The government charcoal, however, shows only 



Fig. 4. 

a slight improvement. In Fig. 4, we note a continued deactivation 
for Sample 16 and activation for U. S. Government 600. This is not a 
disagreement, however, but is an essential difference in the charcoals 
used, resulting from the method of manufacture. In the case of Sample 



Fig. 5. Fig. 6. 



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170 H, NORTON SHELDON, ^5S?S 

16, there are present active carbon, hydrocarbons, and inactive carbon. 
In the government sample, the hydrocarbons have supposedly all been 
removed, leaving only active and inactive carbon. If we are to deactivate 
the government sample, then, we must form inactive carbon from the 
active material, a thing which has not been done when temperatures 
^s high as 1600® C. were usedS* if we are to activate it we must remove 
some of the inactive material, as has apparently been done to some very 
slight extent by the prolonged heating. The deactivation shown for 
Sample 16 is probably due to an inactive deposit on the active material 
as the result of cracking the hydrocarbons at the high temperatures used, 
or possibly the basic structure or active carbon itself was being removed. 

After this treatment outgassings at 500° C. were tried and still found 
to be ineffective. 

The work with hydrogen having completely satisfied the hydrocarbon 
theory, work was begun on nitrogen, and from Figs. 5 and 6 it will be 
seen that there is agreement throughout with predictions made from the 
hydrocarbon theory. 

In this case curve i is the adsorption curve .after a preliminary out- 
gassing only; curve 2 after 15 hrs. at 500° C; curve 3 after g}4 hrs. at 
700° C; curve 4 after 8 hrs. at 800° C; curve 5 after 6 hrs. at 900° C; 
curve 6 after 5 hrs. at 500° C; curve 7 after i hr. at 1000° C; and curve 
8 after 8 hrs. at 700° C. That curves 5 and 6 fall on 2 in Fig. 6, is of 
course accidental. 

In Fig. 7 we have an example of slow oxidation at room temperature 
Curve I is from a run with air taken on Sample No. 9, on July 10, 1915. 
It was then put away and not disturbed until October 10, 1919, when a 
second run given by curve 2 was made. 

Part II. 
The second part of this work consisted, as previously stated, in the 
formation of a charcoal whose adsorption of hydrogen exceeded that of 
nitrogen. This was done merely by heating to 1000° C. for about 3>^ 
hrs. in a vacuum which was kept down by continuous pumping with a 
mercury condensation pump. In Fig. 8, curve i is that of nitrogen, 
and curve 2 that of hydrogen before treatment. Curves 3 and 4 are 
respectively the same after treatment. It will be observed that the 
difference between the amounts of gas, adsorbed in the second case is 
much greater than in the first case. This work was verified with several 
other samples, but, as anticipated, the nature of the U. S. Government 
charcoal made it impossible with this type. 

» N. K. Chaney, ibid. 



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Na*3^^^*] CHARCOAL ACTIVATION, * I7I 

It is obvious then, that there must be a decided difference between the 
adsorption by charcoal of hydrogen and of nitrogen. 

In an article by McBain^ it is shown that hydrogen adsorption, or 
"sorption" as he calls it, takes place in two stages: the first, surface con- 
densation; the second, solid solution. In a later paper by Miss Homfray* 



Fig. 7. Fig. 8. 

the adsorption of several gases and mixtures are studied, with the con- 
clusion that the whole action is that of solid solution, and that two dis- 
tinct stages as found by McBain do not exist. She did not, however, 
work with hydrogen at liquid air temperature. These papers then indi- 
cate a dual action in the case of hydrogen which does not seem to exist 
for other gases, and no contradiction has been found. 

Since the generally accepted theory of adsorption is, at present, the 
surface condensation theory, it seems reasonable to assume this as the 
principal action in the case of both gases, and we might explain the 
apparent difference between hydrogen and nitrogen adsorption as due 
to a secondary action in the first case, which is either a chemical action, 
or as McBain believes, solid solution. 

While it is perhaps difficult to draw a distinct line between solution and 
chemical action, the nature of the substances involved immediately 

> Phil. Mag., 6. 18, 916, 1909. 

* Z. fttr Phys. Chem., 74, 129, 19 10. 



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172 ' H. HORTON SHELDON. [^22s° 

suggests a loose reversible chemical combination between the hydrogen 
and some of the hydrocarbons present, to form hydrocarbons more 
stable at this liquid air temperature. Such an action in the case of 
nitrogen would not be expected. That such an action cannot be with 
the active carbon is evident from the fact that the U. S. Government 
600-minute charcoal could not be put into this condition, and with this 
charcoal the hydrocarbons are supposedly for the most part removed. 

The deposit of inactive carbons on the active bas^ is, according to this 
theory, much more effective in deactivating for nitrogen, since, inter- 
fering with surface condensation, it interferes with the whole effect, 
this not being the case for hydrogen which has the dual nature. The 
observations bear this out. 

A second apparent difference in the adsorption of the two gases is 
shown in the hydrogen curves of Part I. of this paper. While the total 
amount of gas adsorbed was unchanged by the heat treatments from 
400° C. to 600° C, it will be noted that the beginnings of the curves fall 
very rapidly, showing a speeding up of the action, a thing which did 
not take place in the case of nitrogen. The magnitude of the action 
at once dismisses the possibility of the iron tubes used having any 
appreciable part in this. It is suggested that this speeding up of the 
action might be due to an increased fineness of division of the material 
with which the hydrogen supposedly combines, brought about by the 
heating. 

Further work of this sort will be begun shortly and experiments on 
nitrogen and hydrogen mixtures similar to those of Dr. Lemon and Miss 
Blodgett are already in progress by Dr. Lemon and Miss Hepburn. 

The author is greatly indebted to Dr. Lemon for advice and valuable 

suggestions in connection with this work. 

Rybrson Physical Laboratory, 
University of Chicago. 



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Noira^^*] INFRA-RED RADIATION, 1 73 



THE EFFECT OF TEMPERATURE UPON THE TRANSMISSION 

OF INFRA-RED RADIATION THROUGH 

VARIOUS GLASSES. 

By Gb6rgb Rosbngartbn. 
Synopsis. 

Measurements of Infra-red Transmission. — The use of colored glasses as absorp- 
tion screens for transmitting bands of monochromatic radiation depends upon the 
variation in the transmission of the radiation with change in temperature. The 
region investigated extends from i m to 5 m* The temperature was varied from 
40 to 460 degrees centigrade. 

Apparatus; Tungsten Lamp Source, Quartt Spectrometer, and Galvanometer. — 
The radiation from a tungsten lamp was passed through glasses placed in an electric 
heater. The transmission of radiation of various wave-lengths was observed by 
means of a spectrometer using a pair of large rock salt prisms which could be rotated 
through any desired angle and the radiation of varying wave-length made to fall 
on the slit of a thermo-pile. The intensity of radiation was determined by the 
deflection of a highly sensitive galvanometer. 

Conclusions: Transmission Independent of Temperature. — The results appear to 
indicate that to within 8 db per cent, the variation in temperature produces no 
change in the transmission of infra-red radiation through the colored glasses tested. 

THE transmission of infra-red radiation through various glasses has 
been investigated by Dr. W. W. Coblentz^ and others. The 
effect of temperature upon the transmission of the radiation through 
colored glasses has been carried out by K. S. Gibson* for the visible 
portion of the spectrum. 

The present investigation was undertaken for the purpose of measuring 
the change in the transmission for the radiations in the infra-red region, 
extending to about 5 /x, as the temperature of the glass was raised. The 
glasses examined were obtained from the Corning Glass Works through 
the kindness of Dr. H. P. Gage. They are marked with the maker's 
numbers and are similar to those examined by Dr. W. W. Coblentz, the 
transmission curves of which are published in Sci. Paper No. 325 of the 
Bureau of Standards. The size of the glasses ranged from 3 to 5 mm. 
in thickness and about 25 mm. in diameter. 

Apparatus. 

The spectrometer used in the investigation was built in the laboratory 

and is shown in Fig. i. The main feature of the instrument is the use 

» Bulletin 325, Bureau of Stds. 
« Phys. Rev.. Vol. VII.. 1916. 



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174 



GEORGE ROSENGARTEN, 



rSaooND 
LSiRnt. 



of two large rock salt prisms 8 cm. by 1 1 cm. having a refracting angle of 
35 degrees 15 minutes. The prisms are mounted upon a large table so 
as to make angles of 45 degrees with the silvered mirror M3. The 
prism table is caused to rotate about a vertical axis by means of an 
accurate screw which acts upon an arm connected with the table. The 




Fig. 1. 

rotation is measured on a graduated head outside of the box enclosing the 
spectrometer. The radiation enters the spectrometer through a slit 
about }4 mm. in width and falls upon a silvered mirror M i placed 
at a distance of 25 cm. from the slit. The focal length of this mirror 
being 25 cm., the rays leaving its surface are parallel and, falling upon the 
rock salt prism, suffer refraction. When the prism table is properly set, 
the rays enter the prism at minimum deviation and pass through the 
prism perpendicular to the second surface. At the surface of the mirror 
M 3 they are reflected and pass through the second prism emerging at 
an angle of 90 degrees with the direction they had when entering the 




Fig. 2. 

first prism. The rays are brought to a focus by another silvered mirror 
M 2 upon the slit of a thermopile placed at 25 cm. distance. 
The slit, mirrors, spectrometer, and thermopile are all mounted upon 



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Na*3?^^^*] INFRA-RED RADIATION, 1 75 

the same base and placed in a box which was kept closed during each 
set of observations. By turning the screw from the outside the table 
carrying the prism was turned through any desired angle, all other parts 
of the apparatus remaining fixed. At each position of the prisms a 
radiation of a different wave-length was brought to a focus on the thermo- 
pile T,C. I. The thermopile consisted of i6 junction of bismuth and 
silver^ mounted in back of a slit about }4 mm. in width and connected 
with a highly sensitive d'Arsonval galvanometer manufactured by Leeds 
& Northrup Co. The sensitivity of this instrument is rated at 33 mm. 
per microvolt and appeared to remain constant during any set of observa- 
tions. Readings were made by means of a telescope and scale at a dis- 
tance of 2 meters. 

The general arrangement of the apparatus is shown in Fig. 2. A con- 
stant potential of 105 volts was applied to a tungsten lamp which served 
as a source of radiation. The glass P to be examined was mounted in a 
vertical position on the end of a rod and was introduced into the cylin- 
drical tube forming the heater (H). The glass was heated to different 
temperatures by varying the current passing through a coil of wire 
wrapped around the outside of this cylindrical tube. The heater was 
covered by a cylinder of fire clay. The temperature was determined by 
means of an iron-constantan thermo-couple T,C. 2 introduced into the 
opening alongside of the glass. The cold ends of the couple were placed 
in an ice bath (Z) and connected by copper leads to a galvanometer G 2. 
The reading of this galvanometer was at all times made visible by reflect- 
ing a beam of light from the galvanometer mirror to a transparent scale. 
The apparatus was so arranged that all observations and adjustments 
could be made from the position 0. 

Calibration, — The spectrometer was calibrated by observing the posi- 
tion of certain well-known transmission and emission bands, i.e., the 
maximum emission band of the bunsen flame at 4.4 m» the absorption 
band of a film of water at 3 /i and the position of the sodium line. 
Thermo-couple used in determining the temperature of the heater was 
calibrated by comparison with several high temperature thermometers 
placed in the heater and readings taken simultaneously upon the ther- 
mometer and the galvanometer deflection. From these data a curve 
was plotted and the temperature obtained from a reading on the trans- 
parent scale giving the deflection of the galvanometer. 

Measurements. 
The method of mapping the spectrum was to cause different radiations 
to fall in succession upon the thermopile T.C. i and observing the 

» B. S. Sci. Paper No. 229. 



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176 GEORGE ROSENGARTEN, [^SS? 

deflection produced on the galvanometer G i. With the asbestos shutter 
S I removed, the radiation from the lamp passed through the opening 
in the electric heater and was interrupted by the shutter S 2, The posi- 
tion of the spectrometer table was read on the graduated head of the 
operating screw. By pulling aside the shutter S 2 the radiation passed 
through the slit of the spectrometer, and its intensity was determined 
by the deflection of the galvanometer G i. Several readings were made 
for each position of the prisms with variations of about ^ mm. The 
prisms were rotated through a small angle and the new positions deter- 
mined by a reading on the graduated head. 

The spectrum of the source was first mapped for radiations extending 
from I M to 5 M. the temperature of the heater being the same as that of 
the room. The glass specimen P was then introduced and the trans- 
mission at room temperature determined for each position in the spec- 
trum. By sending a current through the electric heater the temperature 
of the glass was raised to any desired degree. When a steady state was 
reached the transmission was observed at this increased temperature. 

The radiation of the heated parts of the apparatus was considerable 
and in order to determine the transmission of the radiation from the 
source L it was necessary to deduct the effect of the radiation of the heated 
parts. The shutter 5 i was introduced making it possible to cut off the 
radiation from the lamp. For each setting in the spectrum the deflections 
of the galvanometer were observed for the following conditions. First, 
the radiation from the lamp interrupted by the shutter 5 i and only 
the radiation from the heated parts of the apparatus allowed to enter 
the spectrometer. Second, by removing the shutter S i the radiations 
from the lamp and the heated parts of the apparatus allowed to enter 
the spectrometer at the same time. Third, same conditions as the first. 
Fourth, same conditions as the second. By subtracting the average of 
the deflections produced by the heated parts of the apparatus from the 
average of the deflections produced by the lamp and heated parts jointly 
it was possible to determine the intensity of the radiation from the 
lamp transmitted by the glass. 

Measurements were made in this manner for such glasses as the blue- 
purple G 585, blue-green G 584, G 171 IZ and others for temperatures 
up to 500 degrees centigrade. The measurements have been repeated 
a number of times and the change in the percentage transmission with 
the increase in temperature for radiations from I /x to 5 m» if any exists, 
must have been of the same order of magnitude as the instrumental errors. 
Owing to the difficulties involved they were as large as 8 ± per cent. 
The results of a typical set of observations are given in Table I. 



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Vol. XVI.I 
No. 3. J 



INFRA-RED RADIATION. 



177 



Table I. 

Transmission of the Blue-purple Class C 38 s. 





Deflectio&i for Temperature. 


Approx. 


Scale. 


Source. 


4oDef. 


360 Deg. 


460 Deg. 


Percent. 


WaTe-length. 


6.80 


13.5 ram. 


3.0 ram. 


3.2 mra. 


2.8 mm. 


- 6.7 


5.6/1 


7.00 


16.0 


3.0 


3.0 


2.8 


- 6.7 


5.0 


7.20 


20.5 


3.8 


4.5 


3.7 


- 3.3 


4.4 


7.40 


26.2 


5.5 


5.0 


6.0 


+ 9.1 


4.0 


7.60 


32.8 


7.0 


7.5 


8.0 


+ 14.3 


3.6 


7.80 


36.5 


8.2 


8.5 


9.2 


-hl2.2 


3.2 


8.00 


41.0 


11.0 


11.00 


11.2 


+ 1.8 


2.8 


8.20 


50.0 


17.5 


17.0 


18.2 


-h 4.0 


2.6 


8.40 


61.5 


22.5 


22.5 


21.8 


- 3.1 


2.4 


8.60 


62.0 


17.0 


16.8 


17.5 


-h 2.9 


2.2 


8.80 


56.5 


11.0 


11.7 


11.5 


-h 4.5 


2.0 


9.00 


48.0 


8.0 


9.0 


8.8 


-hio.o 


1.8 


9.20 


35.2 


7.2 


7.5 


7.8 


+ 8.3 


1.6 


9.40 


32.5 


6.5 


7.5 


8.2 


+26.0 


1.4 


9.60 


25.8 


7.8 


8.0 


7.7 


- 1.3 


1.3 


9.80 


21.0 


7.5 


7.6 


7.0 


- 6.6 


1.2 


10.00 


18.5 


7.2 


7.0 


7.5 


+ 4.2 


1.1 



The first column indicates the reading on the graduated head of the 
operating screw, the second column is the deflection obtained for the 
radiation from the source L, the third column gives the deflection of the 
galvanometer produced by the transmission of the radiation through 
the glass at the temperature of 40 degrees centigrade, the fourth and 
fifth columns give the deflection at 260 and 460 degrees respectively, the 
sixth column gives the percentage change between 40 and 460 degrees, 
the seventh column gives the approximate wave-length as obtained from 
the calibration curve. 

Observations were also made upon various specimens for a single 
wave-length. The spectrometer was set in position and the transmission 
observed for various temperatures. In this manner no part of the appa- 
ratus was moved after the observations were started. The transmission 
obtained in this manner may be seen in Table II. 

Summary. — The results of the above experiment seem to show that to 
within 8 =b per cent, there is no change in the transmission of the infra- 
red radiation through the glasses observed for the region i /x to 5 m as 
indicated in Table I. The results obtained in Table II. indicate the 
degree of accuracy of the galvanometer readings under similar conditions. 
The change in the transmission for observations at this wave-length 
is much smaller. 

The present investigation was suggested by Dr. W. W. Coblentz who 



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178 



GEORGE ROSENGARTEN, 



fSSCONA 

LSbriks. 



Table II. 

Transmission of Blue-green glass G 584, Approx, Wave-Lenglh 2.6 fi. 



Temp. 


Deflectiofit. 


Heater. 


Total. 


Lamp. 


Mean. 


% Change. 


40^ C 





29.0 


29.0 


29.8 









30.0 


30.0 











30.0 


30.0 











30.0 


30.0 











30.0 


30.0 






135 


6 


30.0 


30.0 


30.5 


+2.3 







31.0 


31.0 











30.5 


30.5 











31.0 


31.0 











30.0 


30.0 






190 





30.0 


30.0 


30.3 


+1.7 







30.0 


30.0 











30.0 


30.0 











30.5 


30.5 











31.0 


31.0 






290 


2.5 


33.0 


30.5 


30.2 


+1.3 




3.0 


33.5 


30.5 








3.0 


33.0 


30.0 








3.5 


34.0 


30.5 








4.0 


33.5 


29.5 






360 


9.0 


39.0 


30.0 


29.5 


-1.0 




9.5 


39.0 


29.5 








8.5 


38.0 


29.5 








8.5 


37.0 


28.5 








8.5 


37.0 


28.5 








7.0 


37.0 


30.0 






480 


29.0 


57.0 


28.0 


29.3 


-1.7 




29.0 


57.0 


28.0 








28.0 


59.0 


31.0 








29.0 


58.5 


29.5 








29.0 


59.0 


30.0 







has shown continued interest in the problem. The apparatus was placed 
at my disposal and set up in the Randal Morgan Laboratory' of Physics 
at the University of Pennsylvania. Suggestions have been made during 
the progress of the work by Dr. Goodspeed and Dr. Richards for which 
I wish to express my appreciation. 



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ffo,'^^^'] ^^^ THEORY OF UNEAR-SINOIDAL OSCILLATIONS. 1 79 



THE THEORY OF LINEAR-SINOIDAL OSCILLATIONS. 

By Hbnry G. Cordbs. 

Synopsis. 

Constant frequency arc discharges; theory assuming direct current supply and arc 
potential drop to remain constant. — ^A vacuum arc is shunted with inductance, capac- 
itance and resistance in series which constitutes a discharge circuit. The arc 
is supplied with direct current through a large inductance. The arc vapor is ion- 
ized and de-ionized at a constant frequency. The variations of potential and current 
in the discharge circuit are termed linear-sinoidal oscillations. Mathematical 
expressions are derived for the following quantities in terms of the priming angle 
and damping angle, viz., the logarithmic decrement, ratio of natural frequency to 
discharge frequency, impedance factor and ratio of the effective discharge circuit 
current to the direct current. These quantities are expressed in terms of trans- 
cendental functions of the angles, hence relations between them are determined by 
means of a chart and a table. Expressions for potentials at the instants of priming 
(critical ionization) and unpriming are given. The relation between the values 
of the direct current and effective currents through the arc and in the discharge 
circuit is established. The actual fluctuation of the direct Current supply is approxi- 
mately determined. The counter E.M .F. of an oscillator having a coupled secondary 
oscillatory circuit varies in a manner similar to the counter E.M.F. of a motor. 

De-ionization of arc vapor; experimental determination of the rate. — An arc is 
extinguished by means of initiating a series of linecH--sinoidal oscillations of de- 
creasing frequency. The values of the priming angle, ratio of frequencies, dis- 
charge frequency, unprimed interval, re-ignition i}otential and other quantities 
are approximately determined for the initial oscillations. An expression for the 
numerical value of the rate of de-ionization is given. 

Stabiliiy of an arc oscillator. — The values of series resistance to produce stability 
depends upon discharge circuit resistance, rate of de-ionization and rate of change 
of the rate of de-ionization. Auxiliary means to produce a constant discharge 
frequency are required to stabilize an efficient arc oscillator for radio signalling. 

A PARTICULAR type of oscillation exists, the theory of which has 
been little developed although it forms the basis for direct 
current impact sustention of oscillating current. No general texjn has 
been applied to an oscillation which consists of two partial sinoidal 
oscillations produced by a direct current and a sinoidal current. During 
the first partial oscillation the potential of the capacitance varies prac- 
tically as a linear function of the time and during the second partial 
oscillation the potential varies as a sinoidal function of the time, hence 
the term **linear-sinoidar* will be used to distinguish this particular type 
of oscillation. 
The theory developed in the following pages cannot be completely 



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l8o HENRY G. CORDES, ^SS. 

realized or verified by experiment but it is nevertheless useful as the 
basis for explaining actual phenomena. As an analogous instance the 
law of falling bodies in a vacuum may be mentioned. This law applied 
to an actual body falling in a vacuum is of little value, but it is a very 
important factor in investigating any phenomena involving the law of 
gravitation. 

The Carnot's cycle of a heat engine is another analogous instance. 
No heat engine can be constructed without friction and heat radiation 
losses, yet the theory of this cycle forms an important factor in the study 
of the heat engine. The theory of linear-sinoidal oscillations will there- 
fore be presented for consideration as an important factor in explaining 
actual phenomena. An experiment will be described and the results 
interpreted by means of the theory developed. 

Figure i shows an arrangement of circuits which, with certain assump- 
tions, forms]^the basis for the principal theoretical deductions. 

In Fig. I the condenser C is discharged at a constant frequency N by 



— ^ 



■J— rofewjw 




Fig. 1. 

ionizing the path from the anode A to the cathode if in a vacuum tube V 
which contains a gas at low pressure. 

The path from -4 to if is initially ionized at the frequency iV^ by a 
spark passing from the auxiliary anode F to the cathode K. The vacuum 
tube V is an electrical check valve which will not allow current to pass 
from if to -4 although an E.M.F. tending to produce an inverse current 
is impressed upon these electrodes. The potential drop through V 
will be considered a constant and its A^alue will be represented by £». 
The valve V is therefore assumed to be a device which discharges C at a 
constant frequency, has a constant potential drop for any value of 
current greater than zero and acts as an electrical check valve. 

The arrangement of Fig. i consists of three circuits which will be called 
the charging circuit, the discharge circuit and the arc circuit. The 
charging circuit consists of a source B of direct current, a line resistance r, 
a line inductance, Lg, a capacitance C, an inductance L, and a resistance 
R. The inductance Lg is large compared to L. The discharge circuit 
is an oscillatory circuit having a capacitance C, a discharger F, an 



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No'a^^^*] ^^^ THEORY OF UNEAR-SINOIDAL OSCILLATIONS. l8l 

inductance L, and resistance R. The arc circuit is the direct current 
circuit B — r — Lg — V short-circuited momentarily by the arc V. The 
period T" of a complete linear-sinoidal oscillation consists of two time 
intervals. During the first interval Tu the arc and discharge circuits 
are closed and during the second interval Tt current flows only in the 
charging circuit. The first interval will be referred to as the primed 
period and the second as the unprimed period. 

Figure 2 shows the variations of potential and current in the discharge 
circuit during a complete cycle of a linear-sinoidal oscillation. The 
amplitude of the potential of C and of the current through L and R 



Fig. 2. 

are measured by distances from the X-axis and time is plotted propor- 
tional to the distance from the F-axis. The current through V is 
measured by distance from the J^'-axis and is the resultant of the currents 
in the arc and discharge circuits. Curve e represents the potential of C 
and curve i represents the current through L and R, A direct current / 
flows into C until the potential of C = £«, at which instant the valve V 
becomes conductive and the potential between the electrodes of the valve 
drops instantaneously to the value £». The quantity of electricity 
flowing into C must equal the quantity flowing out of C therefore the 
shaded area above the X-axis which represents the quantity flowing 
during the discharging period must equal the shaded area below the 
-ST-axis which represents the quantity flowing during the charging period. 
It is assumed that Lg is infinitely large so that the direct current I 
will be constant during a complete cycle. When the amplitude of the 
negative current in the discharge circuit equals I the current through V 
becomes zero. It is assumed that when the current through V becomes 
zero that V becomes instantly and automatically a non-conductor. 



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1 8.2 HENRY C. CORDBS. SSSS! 

Mathebiatical Analysis. 
During the period Ti when the energy in the discharge circuit is free 
to oscillate the following potential relations exist, 

di r idt 

Lj^ + Ri + J -^ + £.»o. (I) 

Let 

R 



«=iz- (^) 



Let 



"=Vzfe-^, = 2T/, (3) 

where / = the natural frequency of the discharge circuit. The solution 
of (i) is 

i = ht"^ sin (w/ — 0) (4) 

where Iq is the maximum value of i when R is considered equal to zero. 
The angle ^ is shown in Fig. 2. 

At the instant / = o when the discharge circuit becomes free to oscil- 
late a negative current / flows in the discharge circuit. Substituting 
these values in (4), 

7 = /o sin <^. (5) 

At the instant / = 7*1 the discharge circuit ceases its free sinoidal 

oscillation while a negative current I is flowing. Again substituting 

in (4). 

- / = /oe-*^ sin (u)Ti - <A). (6) 

Equation (6) can be written in a more convenient form by letting 

o)Ti^2it> + h + T, (7) 

which substituted in (6) gives 

/ = /oe-**^ sin {<^ + h). (8) 

Equating potentials in the discharge circuit when / = o gives 



[4] 



+ [Ri]^-^ - £a + £. = o. (9) 



From (2), (5) and (9) 

Ea =* coLZ cot <l> - oLI + £„. (10) 

Equating potentials in the discharge circuit when t = Ti gives 

^dt\ + ^^'^'^'^ + £5 + £. = o. (II) 

From (2), (7), (8) and (11), 

Eb = uLI cot ((t> + h) + oLI - £,. (12) 



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No^il^^'] ^^^ THEORY OF LI NEAR-SI NOI DAL OSCILLATIONS. 1 83 

Equating the quantities of electricity flowing during the primed and 
unprimed periods will give the equations 

f idt^ {Ea + Et)C (13) 

Jo 
and 

{Ea + Ef)C = ITt. (14) 

Adding (10) and (12), 

£a + £5 = «L/[cot 4* + cot {4> + h)]. (15) 

From (14) and (15) 

where the logarithmic decrement 



_, cot » + cot (» + h) I ... 



« = . (I7> 

CO 

From (7) and (16), 

r 7^ ^7^ cot » + cot (» + &) I 2» + A + T 

<a I + {o/27ry w 

Let 

^=1^=-. (19) 

where N = the discharge frequency, or frequency of the Hnear-sinoidal 
oscillations. Then, 

, cot * + cot (* + A) I 2<l, + h + T 

* ^ rrw^iri^'^ — ^ — • ^^''^ 

In order to evaluate the angles ^ and h the quantities ^ and h must be 
known. The value of h can be expressed in terms of 4> and A. 
From (5) and (8), 

«-"•■ - ■ 1 1 .^ • (^0 

sin (^ + A) ^ ' 

From (7) and (17), 

«r. = (^ — T^ — j«- («) 

From (21) and (22), 

^ log sin {4> + h) - log sin , . 

27r 2 

The values of and h can be determined from the values of ^ and 5 
by means of a chart. Figs. 3 and 4 are charts in which the ordinates 
represent the values of and the abscissas represent the values of A. 



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184 HENRY G. CORDES. ^S^ 

A number of 5-curves are plotted. Values were assigned to ^ and h in 
(23) and a series of values of 6 were calculated. This series was used to 
obtain, by interpolation, values of and h for given values of 6 which 
are 0.02, 0.04, 0.06, 0.08, o.i, 0.12, 0.16, 0.2^ 0.3, 0.4, 0.5, 0.6, 0.8, i.o, 
1. 12, 1. 16, 2.0 and 3.0. 

A similar series of curves are plotted for values of ^ calculated from 
•equation (20). Curves representing values of ^ for i.ooi, 1.003, 1-005, 
-1 .01, 1.02, 1.03, 1.05, 1.07, 1. 10, 1. 14, 1.2, 1.3, 1.5 and 2.0 are shown. 

Figures 3 and 4 will be referred to as the 0-A chart. Every point 



Fig. 3. 

on this chart represents one value of 0, h, 8 and ^. Any two of these 
quantities will determine a point on the chart therefore when 8 and ^ 
are known the corresponding values of and h can be found. The 
quantities L, C, R and N determine the values of <t> and h. 

The variation of A as a function of the damping of the discharge circuit 
current is illustrated in Fi^. 5. The current of equation (4) is represented 



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5^3?^^'] ^^^ THEORY OF LINEAR-SINOIDAL OSCILLATIONS. iSS 

by means of polar coordinates. The curve representing the current 
approaches a circle as the damping approaches zero. The outer spiral 
represents the current in a discharge circuit whose logarithmic decrement 
= 0.4 and the inner spiral is a current whose decrement = Q.83. The 



Fig. 4. 

line Jf — Z is parallel to the polar axis and its distance from the polar 
axis represents the amplitude of the direct current. The priming angle 
is the angle between the polar axis and a line drawn from the pole to 
the intersection of the line X — X and the circle. The damping angle h 
is the angle between the lines drawn from the pole to the intersection 
of the line X — X with the circle and with the spiral. The unprimed 
period cannot conveniently be illustrated by means of polar coordinates. 



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1 86 



HENRY G, CORDES. 



fi*pr— 



The polar axis and line X ^ X must be rotated positively about the 
pole through an angle of wr — 27r radians between the instants of 
extinction and re-ignition to represent the unprimed period. 
The largest value that b and h can have for a given value of is deter- 




Fig. 5. 

mined by the maximum negative amplitude of i in equation (4). This 
occurs when 

5i = 27r cot (01 + h). (24) 

If b is greater than this value the valve V will not unprime and the 
capacitance C cannot be charged. The valve V will then practically 
form a permanent short-circuit on the line. 

The extinction limit curve on the <f>'h chart is the locus of points 
obtained by substituting equation (24) in (23). Any one of the three 
variables may be eliminated. Table I. gives values of these variables 
from which the extinction limit curve was drawn. The angle ^ + A 
was eliminated, values were assigned to bi and values of ^i were easily 
found by interpolation. 

Given the quantities L, C, R, N, I and £» the value of £, and £» 
can be determined with the aid of the 4>'h chart from equations (10) 
and (12). 

The maximum potential £«, impressed upon the capacitance C can 
also be calculated by the gi\'en quantities by the relation expressed by 



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Na"3?^^'] ^^^ THEORY OP UNEAR-SINOIDAL OSCILLATIONS, 

Table I. 



187 



»l. 


^ + A. 


^. 


»i. 


^ + A. 


^. 


»i. 


^ + A. 


^' 


0.01 


89* 55' 


82** 


r 


0.7 


83** 38' 


33"* 


52' 


2.4 


69** 6' 


9** 35' 


0.02 


890 49/ 


78^ 


46' 


0.8 


82** 45' 


31** 


5' 


2.5 


68** 18' 


8** 57' 


0.03 


89'' 44' 


76» 


17' 


0.9 


81** 51' 


28** 


37' 


2.6 


67** 31' 


go 22' 


0.04 


89** 38' 


74« 


16' 


1.0 


80** 57' 


26** 


24' 


2.7 


66** 45' 


7** 50' 


0.05 


89** 33' 


72** 


29' 


1.1 


80** 4' 


240 


24' 


2.8 


65** 59' 


70 19/ 


0.06 


390 27' 


70** 


53' 


1.2 


79** 11' 


22** 


35' 


2.9 


65** 13' 


6** 51' 


0.07 


89* 22' 


69** 


26' 


1.3 


78** 19' 


20** 


56' 


3.0 


64** 29' 


6** 24' 


0.08 


89'* 16' 


68** 


5' 


1.4 


77** 26' 


19** 


25' 


3.1 


63** 44' 


6** 0' 


0.09 


89** 11' 


66** 


50' 


1.5 


76** 34' 


18** 


3' 


3.2 


63** 1' 


5** 37' 


0.10 


89^ 5' 


65** 


42' 


1.6 


75** 43' 


16** 


47' 


3.3 


62** 17' 


5** 15' 


0.12 


SS"* 55' 


63** 


26' 


1.7 


74** 52' 


15** 


37' 


3.4 


61** 35' 


4** 55' 


0.16 


88** 33' 


59** 


46' 


1.8 


74** 1' 


14** 


32' 


3.5 


60** 53' 


4** 36' 


0.20 


88** IV 


56** 


34' 


1.9 


73** 11' 


13** 


33' 


3.7 


59** 24' 


4** 5' 


0.30 


87** 16' 


50** 


4' 


2.0 


72** 21' 


12** 


38' 


4.0 


57** 27' 


3** 22' 


0.40 


86** 21' 


44** 


56' 


2.1 


71** 31' 


11** 


47' 


5.0 


51** 29' 


1** 45' 


0.50 


85** 27' 


40** 


40' 


2.2 


70** 42' 


11** 


0' 


7.0 


41** 55' 


0** 30' 


0.60 


84** 34' 


37** 


2' 


2.3 


69** 54' 


10** 


16' 


10.0 


32** 8' 


0** 5' 



equation (i) when / = 0/w which is 



btr- 



+ m<-l-E„ + E, = o. 



Solving (25) for £« gives 






(25) 



(26) 



which shows that for given values of L, C, / and £» the value of £«, 
varies practically inversely as sin <t> which depends upon the discharge 
frequency N, 

When RI and £, are small compared to Em and Ea the ratio of £« 
to Em varies practically as cos which shows that Em becomes very 
large compared to Ea as approaches ir/2. 

The maximum value of current * in equation (4) is 

Direct Current Impedance. 

The average counter E.M.F. of the capacitance C during the interval 
of time Tt is represented by the ordinate of the middle point of the straight 
line connecting the points Eb and Ea in Fig. 2. From (10), (12) and (17), 

Ea-Eb^ 

2 



-^^ I cot - cot (0 + A) - - 






+ £,. 



(28) 



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1 88 HENRY G. CORDES, 

The potential drop due to current / flowing through resistance R 

during Ti is 

S 
IR ^ 2otLI ^ (jiLI - . (29) 

T 

The total average E.M.F. consumed by the oscillator during Tt is 

^° J^' + /Jg = ^[cot * - cot (« + A) +^] +£•. (30) 

The E.M.F. consumed by the oscillator during Ti is £». The E.M.F. 
impressed upon the terminals A and K of the valve V is equal to the 
average E.M.F. consumed by the linear-sinoidal oscillation, or, 



From (30) and (31) 

From (i6) and (32) 
£-■£,- /r 



(31) 
(32) 



[X . ,x . «1cot* + cot (*+A) I , , 

cot«-cot(«+^)+;J -J.—^-^^^^,. (33) 



Let 

. E-E,-Ir 



Then 



^ r , . ,N . 51 cot * + cot («+A) I , , 

^=[cot*-cot(*+A)+-J _^^-^^^^,. (35) 



Equation (34) may be written 



= po^L + r. (36) 



The term fia>L will be referred to as "impedance" since it impedes the 
flow of direct current to the oscillator. The impedance depends upon 
the quantities L, C, R and the discharge frequency. For a given value 
of L, C and R the impedance increases as N decreases. For a given value 
of L, C and N the impedance will increase as R is increased. Decreasing 
either L or C while the other three quantities remain constant will 
increase the impedance. 

During each cycle the energy delivered to the terminals of the valve 



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Nc^3?^^'] ^^^ THEORY OP LINEAR-SINOIDAL OSCILLATIONS, 1 89 

equals the energy stored or dissipated in the valve and discharge circuit, 
or, 

(£ - Ir)IT + \CEt? = \CEa^ + PRTt + IE,Ti. (37) 

The relation expressed by (37) can also be derived from (14) and (31). 
The discharge circuit capacitance C returns energy to the charging 
circuit from the instant the arc is extinguished until the potential of C 
becomes zero. 

Effective Current. 

The effective current of a linear-sinoidal oscillation can be expressed 
by two equations. The first equates the energy delivered to the linear- 
sinoidal oscillations and the energy dissipated by the oscillations, which 
is 

(£ - /r - £,)/ = la^R, (38) 

where /« is the effective linear-sinoidal current which may be measured 
with a hot-wire ammeter placed in series with the discharge circuit 
capacitance. 

The second equation expresses the fact that the square of the effective 
current is equal to the average value of the square of the instantaneous 
current during a complete cycle, which is 

/.» = [pr, + jr i?dt\j., (39) 

^ T 4aT ^* J' 

^0* r -tj « sin 2(w/ — ^) — <* cos 2{ut — ^) T* , ^ 

"ifL*" ^T^^^ J.- ^^°^ 

From (16) 

PTt P [ cot » + cot (0 + h) I 1 

T ~ Tl ■ « ' I + («/2t)«J* ^'^'^ 

From (5), (7) and (21) 

~f I*-*^]? = £f [cot« (* + *)- cot« 4,]. (42) 

From (5), (7) and (21) 

i£[ -t^T, " sin 2(o)Ti — 4t) — a cos 2{wTi — ») "I 

4^1* «* + «* J 

7* 
= ^p(^ ^ ^) [2« cot (« + A) - a cot* (* + A) + a]. (43) 



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IQO HENRY G. CORDES. ^SSS 

From (5), 

li. ^ ^^" ^"" ^^^ "" ^ ^^^ ^^ ^^^ 
4r a> + w« 

= 42-(^ + ctf^) f" - 2w cot « - a cot* «]. (44) 

Substitute (41), (42), (43) and (44) in (40) and let 

7=y, (45) 

then the result reduces to 

, fcot « - cot (« + A) , I "1 cot « + cot (« + h) I , ,, 

•^ =L ~1 +7j -^^ I + («/2.)»- (4^^ 

A very interesting and important relation exists between 7 and /8. 
From (35) and (46) 

7» = -^ -iS. (47) 

A simpler and easier method of deriving equation (46) is as follows: 
Equation (38) may be written 

^-^ -^^R^r^ (48) 

Then (47) can easily be derived from (36) and (48). Substitute (35) in 
(47) and the result will be equation (46). 

Each of the quantities ^, 5, /8 and 7 have been expressed as functions 
of the angles and A. Any two of these six quantities will theoretically 
determine the remaining four. The angles and A are useful only in 
plotting curves and in establishing relations among the other four 
quantities. A complete • h chart should also have /8-curves and 7-curves 
plotted upon it. 

The 7-curves have been found to be practically parallel to the ^- 
curves, that is, the members of equation (47) remain nearly constant 
for a given value of ^ when R is varied. The consequence of this rela- 
tionship is that 0, A, h and /8 cannot be determined from values of ^ 
and 7 but that practically only one value of 7 exists for a given value 
of ^ over a large range of discharge circuit decrements. Hence the natural 
frequency / can be determined from values of the direct current /, the 
effective current /« and the frequency N of the oscillations. 

Table II. (^-7 table) shows values of ^ and the corresponding values 
of 7. For each value of ^ two values of 7 are given; one value, 70, is 
given for zero damping and another value, 71, for maximum damping, 
i.e., at the intersection of the ^-curve with the extinction limit curve. 



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Vou XVI-l 



THE THEORY OP LINEAR-SINOIDAL OSCILLATIONS. 

Table II. 

^ . y Table. 



191 



f. 


70. 


71- 


^. 


70. 


71. 


1.000 


0.71 


0.71 


1.14 


1.04 


1.01 


1.001 


0.72 


0.72 


1.2 


1.13 


1.10 


1.003 


0.74 


0.73 


1.3 


1.25 


1.21 


1.005 


0.75 


0.74 


1.4 


1.35 


1.32 


1.01 


0.77 


0.76 


1.5 


1.44 


1.42 


1.02 


0.81 


• 0.79 


1.6 


1.53 


1.51 


1.03 


0.84 


0.82 


1.7 


1.61 


1.60 


1.05 


0.88 


0.86 


1.8 


1.69 


1.68 


1.07 


0.93 


0.90 


1.9 


1.77 


1.76 


1.10 


0.98 


0.95 


2.0 


1.84 


1.83 



When A = o in equation (46) the value of the resulting indeterminate 
expression is 

which value 7 approaches as d approaches zero. As ^ approaches unity 
7* approaches the value 0.5 which value is obtained by substituting ir/2 
for <t> in (49). The impedance y^R varies directly as R provided the 
discharge frequency is constant. For values of 7 less than unity an 
ohm of resistance in the discharge circuit will impede the flow of direct 
current less than an ohm in the direct current circuit while for values 
of 7 greater than unity resistance is more effective in the discharge 
circuit. The value of ^ corresponding to 7 = i is about 1.12. 

The simple relation expressed by equation (47) and the fact that the 
7-curves are nearly parallel to the ^-curves render /8-curves and 7-curves 
unnecessary upon the 0-A chart. 

The average current through the valve F" is / and the effective current 
through V can be calculated from the values of / and /a. Let h = the 
effective current through V, then 



From (13) and (14) 



I r^ 

Ii? = fj (i + D'dt. 
Jo 



idt = ITt. 



Substituting (39) and (51) in (50) gives 

/6* = /<.* + P. 



(50) 
(51) 

(52) 



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192 HENRY G. CORDES, [|SS 

Valve Potentials. 
The maximum potential impressed upon the valve F is at the instant 
of re-ignition, i.e.^ at the beginning of the period Ti, Let £1 represent 
the value of this potential, then 

£1 = £a + IR. (53) 

From (10) and (53) 

£1 = oiLI cot + otLl + £„. (54) 

Let £1 = the maximum potential tending to produce inverse current 
through the valve, then 

£2 = £5 - IR. (55) 

From (12) and (55) 

£2 = <aLI cot (« + A) - oLI - £.. (56) 

Equations (10), (12), (54) and (56) may be written in the form 



£a = coL I cot « - ^ J / + £„ 

£5 = wL I cot (« + A) + — J / - £., 

£1 = coL I cot « + —[/ + £., 

£2 = wL cot (0 + A) / - £p. 



(57) 
(58) 

(59) 
(60) 



The coefficients of / in these equations depend upon L, C, R and N. 
Assuming £» comparatively small, these equations show that the poten- 
tials £«, Eh, £1 and £2 vary practically directly as the direct current /. 
The values of these potentials can be found when any two of the six 
quantities ^, 5, /8, 7, ^ and A are known except ^ and 7. Equations 
(57) » (58), (59) and (60) considered in connection with equation (36) 
or (48) show that these potentials vary practically directly as the average 
potential £ provided L, C, R and N remain constant and £» is com- 
paratively small. 

Direct Current Fluctuation. 

The theory of linear-sinoidal oscillations is based upon the assumption 
that the line inductance Lg is infinitely large which is equivalent to 
assuming that the period 2ir^LgC is infinitely long. The charging 
circuit is an oscillatory circuit in which a partial sinoidal oscillation takes 
place during the unprimed period T2 of each oscillation. The current 
flowing through 5, r and Lg is the resultant of a direct current of constant 
amplitude and a linear-sinoidal oscillating current of comparatively 
small amplitude. 



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Vou XVI.1 
Naa. J 



THE THEORY OF LINEAR-SINOWAL OSCILLATIONS. 



193 



Figure 6 shows a curve representing the oscillating component of the 
current. This component is represented by a nearly straight line 
during the time interval Ti and a sinoidal curve during the interval T^. 
During the primed period Ti the rate of change of the current in the 
arc circuit is practically a constant provided r is small. During the 
unprimed interval the rate of change of current depends largely upon 
the potential of the capacitance C. A suggestive name for the oscillating 




UfcT- 



Fig. 6. 

component is *' sinoidal-linear " oscillation since the periods of linear 
and sinoidal variations of current in Lg and L are interchanged. 

Let Lc — Lg + L = the inductance of the charging circuit. Let 
fe — R + r = the resistance and ai = the damping factor. Letcoo/27r = 
the natural frequency of the circuit. 

In Fig. 6 let the current 

to = /xc~**' cos Wo/, (61) 

where /, is the maximum amplitude of the current in the charging 
circuit. Let T, = the time between maximum value /, and the mini- 
mum value In of the current, to, then 

In = /x€—'''COS Wo^,. (62) 

The equation of potentials in the charging circuit when / = T, is 

E - [ic^']'''^'- Infc - £a = O. (63) 



From (62) and (63) 



Infc 



E + WoLc V/,2,-2«xr.. J^2^^^Ea^ o. 



(64) 



For large Lg and small r, r^^^' = i and /, + /* = 2/ approximately. 
Let Al represent the current fluctuation. 
Then A/ = /, — /« which is negligible when compared to /. Under 



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194 



HENRY G. CORDES. 



these conditions equation (64) becomes 



Ire 



or 



E + «oLe V2/A/ ^ - £« = o 

2 



.,.[B.-B+f-]'.^,. 



rsccoMD 
ISssns. 



(65) 



(66) 



The current curve of Fig. 6 is similar to the potential curve of Fig. 2 
while the potential variations between the terminals of Lg are similar to 
those between A and K oi V shown in Fig. 2. The ordinates of Fig. 6 
are drawn to a much larger scale than the ordinates of Fig. 2. 

Experiments. 
A few experiments were made with available apparatus at the Uni- 
versity of Washington by Mr. T. M. Libby to experimentally verify 




Fig. 7. 

phenomena predicted from the theory of linear-sinoidal oscillations and 
to determine the rate of de-ionization of mercury arc vapor. 

Figure 7 is a diagram of connections of the experiments. A ten- 
ampere arc rectifier was used for a discharge valve V. Current was 
started from the anodes to the cathode by means of switch St and tilting 
V. The mercury vapor in V was raised to the proper temperature by 
passing about five amperes from each anode to the cathode for several 
minutes. The switch ^3 was then also opened. The line inductance Lg 
consisted of the secondaries of two 220-2200 r. — 10 K.W. iron-core 
transformers. The discharge circuit condenser C was charged to a 
potential £,• and was then discharged through R and L by means of 
switch Si, This discharge of C extinguished the arc provided R was 
small enough, and the potential £» was sufficiently high. 

The extinction of the arc is explained in terms of the theory as follows. 
The discharge of C unprimes the valve for an interval T2, The length 
of T2 depends upon / and the potential d between anode A and cathode K 



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NoTa^*] ^^^ THEORY OP UNEAR-SINOIDAL OSCILLATIONS. I95 

required to re-ignite the arc, that is, e\ initiates a primed interval Ti. 
The arc is therefore extinguished by initiating a train of linear-sinoidal 
oscillations of decreasing frequency. The length of the train depends 
upon the electromagnetic energy stored in the line inductance Lg. 
In Fig. 7 let fo + fi = r, then 

E'-E.^If (67) 

when a constant direct current / is flowing. 

By unpriming the valve with the discharge of C a direct current 
impedance y^R is introduced into the d.-c. circuit so that for an instant 
equation (67) becomes 

- L,^+ £ - £. = T^i?/ + fl. (68) 

From (67) and (68) 

Equation (69) shows the rate at which the direct current starts to 
decrease when the energy consumed by R per cycle is small compared 
to (LgP)/2, that is, when the period of a linear-sinoidal oscillation is 
short compared to the duration of a train of oscillations. 

Assume, contrary to fact, that ei remains constant during a train of 
oscillations. The decrease in / due to the introduction of y^R increases 
the ratio Ti/T and the time Tt required to re-ignite the arc. Since 7 
increases with this ratio it is seen that the introduction of impedance 
decreases / and the decrease of / in turn increases the impedance and 
so on until the arc is extinguished. 

In fact d increases rapidly as / decreases because the potential of C 
rises more slowly which increases Tt and this gives the arc vapor more 
time to de-ionize so that the final re-igniting potential Ci of a train of 
oscillation is very high. 

The value of the re-igniting potential ei in the experiment rose during a 
train of oscillations to the potential required to disrupt about an eighth 
inch air gap. The distributive capacitance of inductance Lg which is 
equivalent to a capacitance in parallel with Lg required the presence of 
the protective condenser shown. The maximum and final value of ci 
varies with Lg and with the rate of de-ionization of the arc vapor. 

For a given value of /, £,-, C and L in Fig. 7 there is a maximum value 
of i? ( = Ri) which will allow the discharge of C to extinguish the arc. 
Assume, contrary to fact, that the potential difference between A and K 
remains constant until the arc current is reduced to zero then the mini- 
mum value of Ei which will reduce the current to zero is determined by 



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196 HENRY G. CORDES, ^^ 

the energy stored in the condenser minus the energy dissipated by trans- 
forming the electrostatic energy into electromagnetic energy which gives 

£, (min.) = lyj^'J^^^'"^^ esc (cot"^^) , (70) 

where di corresponds to Ri. Since the potential drop does not remain 
constant between A and K for small currents the actual value of £,• will 
be less than the value necessary to satisfy equation (70). 

In the experiment Fig. 7 the quantities £, £» and Et were measured 
with a voltmeter, / with an ammeter and L and C with a wavemeter. 
The resistance R consisted of fine wire whose high frequency value was 
known. The values of these quantities were : C = o.oi m.f.,/ = 316,000, 
o)L = 50.4 ohms, Ri = 18 ohms, di = 1. 14, / = 5 amperes, Ei (+ leak- 
age) = 450 volts and £» = 13 volts at from 2 to 10 amperes of steady 
arc current. 

From the above data all the quantities of the initial linear-oscillations 
of a train can be approximately determined. The initial value of the 
re-igniting potential d of a train of oscillations can be found by sub- 
stituting ei for £1 in (59) which gives 

Ci = o)L(cot<l>i+^jI + E,, (71) 

where 0i is the value of at the point where the 5-curve intersects the 
extinction limit curve. The value of 0i on the ^-A chart at the point 
where 5 = 1.14 is about 23 J degrees. Substituting this value in (71) 
and solving for ei gives Ci = 623 volts. On the <f>'h chart when ^1 
= 23^°, then ^1 = 1. 17 and from the ^-7 table 71 = 1.05. Let n = the 
variable discharge frequency, then the initial discharge frequency no 
substituted in equation (19) for N gives «o = 370,000 cycles per second. 
From equations (16) and (24) T2 = 1.18 micro-seconds. The values of 
variables Cai Cb and 62 corresponding to £a, £5 and £j in equations (57), 
(58) and (60) are Ca = 530 volts, Cb = 78 volts and ^2 = — 13 volts for 
the initial oscillations. 

The ratio ei/T^ may be considered a measure of the rate of de-ionization 
of the arc vapor under given conditions. This ratio will be influenced 
by the manner and time required to reduce the arc current to zero before 
the potential between A and K starts to rise practically as a linear 
function of the time. Both the magnitude of €2 and the duration of a 
negative potential upon valve V will affect the value of the re-igniting 
potential ei. 

When C was increased from o.oi to 0.04 m.f. and R was small the 
minimum value of £,• (+ leakage) required to extinguish the arc was 



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No'a^^^*] ^^^ THEORY OF LINEAR-SINOIDAL OSCILLATIONS, 1 97 

reduced from 450 to 240 volts or less. The value of Ri became more 
critical as the capacitance C was increased. An increase of £» resulted 
in requiring a larger Ri to extinguish the arc. This result was expected 
from the fact that the initial 2^2 was increased by increasing Ei which 
gave the arc vapor more time to de-ionize and thereby increased the 
initial value of Ci and decreased the initial discharge frequency. 

The results of this experiment are only approximate due to the fact 
that (i) the potential drop between anode and cathode does not remain 
constant for small values of arc current which gives too large values for 
Ri\ (2) the value of Ri depends upon Ri whose value depends upon 
leakage during the time required to throw switch ^4; and, (3) the presence 
of high-high frequency oscillating current transients which flow in the 
oscillatory circuit formed by the capacitance between, and the inductance 
of, the leads to the anode and cathode or which flow through the dis- 
tributive capacitance of Lg and protective condenser in series. The 
dielectric of a o.oi M.F. condenser must have a resistance of 2,400 
megohms in order that its charge be reduced only twenty per cent, in 
one-tenth second of isolation. No special precautions to reduce leakage 
were taken. It is proposed to overcome this unknown leakage by 
permanently connecting the source of Ei to C through high inductance 
and high resistance and extinguishing the arc by closing a S.P-S.T. 
switch in the discharge circuit. 

An attempt was made to measure the initial value of n with a wave- 
meter but the impulse of the final oscillations of a train destroyed the 
cumulative effect of the initial oscillations. The effect of intensity above 
a limited value must be eliminated and the cumulative effect must be 
retained. A special arrangement is required to secure this result. It 
may be noted that extinction of the arc developed a high potential be- 
tween turns of the discharge circuit inductance L; this was attributed 
to the final discharges of a train. 

Stability of Linear-Sinoidal Oscillations. 

Stability of linear-sinoidal oscillations can be produced by either 
providing a properly timed priming spark or by increasing the potential 
E of the d.c. source and the series resistance r to a sufficiently high value. 

The later method will be considered. In order to have stability in 
any mechanical, electrical or other system in which energy is supplied 
and consumed, the requirement for stability is that the rate of change of 
energy consumption with respect to an independent variable must be greater 
than the rate of change of energy supply with respect to the same variable. 
This criterion will be applied to the arrangement of Fig. 7. 



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198 HENRY C, CORDES, [ll^ 

Differentiate equation (38) with respect to / and from the resulting 
diflferential equation and (38) the critical series resistance is 

A resistance greater than this value is required to produce stability. 
The Pr loss may be considered as either decreasing the energy supply 
or increasing the energy consumption. In equation (72) the value of 
dia/dl depends upon the rate of change of the rate of de-ionization. 
The value of r increases as the rate of change decreases. The rate of 
change probably depends upon the rate of de-ionization. The rate of 
change will be negative when /« increases as / decreases and positive 
when la decreases as / decreases. The initial value of ei of a train 
varies with the rate of de-ionization and as this rate is decreased in- 
creases and 7 and R must be less, hence critical r varies with rate of 
de-ionization. 

The values of <t> and A of a train are determined by a 5-curve. In the 
experiment <t> and h are determined by the locus of points on the ^-A 
chart at which S = 1.14. The duration of a train is decreased as R 
and 7 are increased and as the rate of change is decreased which results 
in increasing the rate of energy consumption and decreasing the total 
energy consumed per train. 

These interpretations of equation (72) appear to explain the cause for 
the greater instability of an arc when the temperature of the arc vapor 
is low and the rate of de-ionization is high. There is always a small 
capacitance and inductance externally between the anode and cathode 
of an arc due to the connecting leads. The slightly drooping volt- 
ampere characteristic and the low resistance of such an oscillatory 
circuit will produce sinoidal oscillations of sufficient amplitude to reduce 
the arc current to zero and thus initiate a train of unstable linear-sinoidal 
oscillations. 

Inductively Coupled Secondary Circuit. 

Energy can be withdrawn from the discharge circuit by coupling a 
secondary oscillatory circuit to the inductance L, to the capacitance C 
or to the valve V. Figure 8 is the same as figure i with the addition of a 
secondary circuit Lt — C2 — fs coupled to the inductance L. The 
presence of the secondary circuit reduces the effective inductance, and 
increases the effective resistance, of the discharge circuit. The direct 
current impedance is increased by either increasing o) or R therefore 
current flowing in the secondary circuit increases the impedance. The 
^•7 table shows that the impedance y^R increases with R when ^ and N 



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Vol. XVI. 
No. 3. 



] THE THEORY OF UNEAR-SINOIDAL OSCILLATIONS. 1 99 



remain constant. When R and N are constant the table also shows that 
an increase in ^ due to an increase in co correspondingly increases 7. 

The arrangement of Fig. 8 can be compared to a direct current motor. 
Let the energy consumed in the secondary circuit be compared to the 
load placed upon the motor shaft. When the motor shaft cannot turn 
no powtfr is delivered to the shaft and a heavy direct current flows 
through the armature resistance. A similar condition exists in Fig. 8 



j-wwyw^^ 



5 



"^^-^OOOOOO'OOMO: 




Fig. 8. 



when the resistance fi is infinitely large and the resistance R is similar to 
the armature resistance. As ri is reduced, current flows in the secondary 
circuit, the effective value of w becomes greater and the impedance be- 
comes greater with a corresponding decrease in the direct current. As 
the motor shaft begins to turn a counter E.M.F. is generated which de- 
creases the current. If fj be made zero the impedance will become large 
and little current will flow which is analogous to the d.c. motor with 
no load. 

In Fig. I if Ir is placed in series with the valve V instead of in series 
with C and R the theory developed in the preceding pages will apply 
except the fluctuation of the direct current. The maximum potential 
producing fluctuation would be increased from Ei to £«,. 

References. 

The theory developed to explain the phenomena of arc oscillators 
described in the Physical Review (Vol. VI., No. 6, pages 450-469) by 
B. Liebowitz and in the Proceedings of the Institute of Radio Engineers 
(Vol. 5, pages 255-316) by P. O. Pedersen is based upon experimental 
results. 

The vacuum-arc oscillator proposed by Liebowitz depends upon a 
large series resistance and a high potential source of direct current to 
produce stable oscillations. This arrangement is inefficient and high 
potential is undesirable. 

The Poulsen arc oscillator is stabilized by means of an arc whose 



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200 HENRY G, CORDES. [smmou 

volt-ampere characteristic has a steep slope, the value of the angle 4> 
is large and the rate of de-ionization is small compared to a vacuum-arc. 
This oscillator requires a comparatively high potential direct current 
supply and the arc loss is large. 

The theory of linear-sinoidal oscillations indicates that efficient arc 
oscillations can be produced by providing a constant frequency*priming 
spark. The series resistance or arc loss required to secure stability 
can thereby be avoided. 

The rate of de-ionization of arc vapor when an arc has been extin- 
guished depends upon the velocity with which ions recombine and 
probably also upon the rate of cessation of the ionizing effect of the 
incandescent cathode and vapor. Reduction of gas pressure facilitates 
recombination of ions. Lowering the temperature of the vacuum tube 
decreases the gas pressure and probably reduces the ionizing effect due 
to incandescence of the gas. 

Little appears to be known regarding the law governing the rate of 
de-ionization of arc vapor as influenced by the composition and pressure 
of the vapor or gas. The law of this phenomenon has practical applica- 
tion in radio signalling and may extend knowledge of the electron theory. 
In addition to showing an application of the theory it is believed that 
the experirfient described in this paper is the first attempt to measure 
the rate of de-ionization of arc vapor. 

Bremerton. Wash., 
April, 1920. 

List of Principal Symbols. 

C Capacitance of discharge circuit condenser. 

L Inductance of discharge circuit inductance. 

R Resistance of discharge circuit. 

Lg Inductance in series with d.-c. source. 

r Resistance in series with d.-c. source. 

/ Natural frequency of discharge circuit. 

N Discharge frequency. 

/ Direct current. 

la Effective discharge circuit current. 

E E.M.F. of d.-c. source. 

Ea Potential of C at instant of re-ignition. 

Eh Potential of C at instant of extinction. 

El Potential between anode and cathode at instant of re-ignition. 

Et Potential between anode and cathode at instant of extinction. 

Ev Potential drop of current through arc. 

T rime of one complete oscillation. 



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nS"3^'*] ^^^ THEORY OF LINEAR-SINOIDAL OSCILLATIONS, 20I 

Ti Time of primed period. 

Ti Time of unprimed period. 

<f> Priming angle. 

h Damping angle. 

8 Logarithmic decrement of discharge circuit. 

a Damping factor of discharge circuit. 

^ Ratio of frequencies. 

fi Impedance factor. 

y Ratio of currents. 

a) 2irf. 



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202 HUGO FRICKE. ^SS! 



THE K-CHARACTERISTIC ABSORPTION FREQUENCIES FOR 

THE CHEMICAL ELEMENTS MAGNESIUM TO 

CHROMIUM. 

By Hugo Fricke. 

Synopsis. 

Absorption of X-Rays, — This paper contains an account of an experimental in- 
vestigation concerning the discontinuity in the X-ray absorption corresponding 
to the K-series for the chemical elements from magnesium to chromium inclusively. 
The method followed was the same as that devised and employed by de Broglie. 
A specially designed vacuum spectrograph was used. 

Fine Structure of Absorption. — The spectrograms show that the discontinuity has 
a rather complex structure, a result in advance of those obtained by earlier investi- 
gators. A photometric study of the plates was made in order to obtain a more 
accurate knowledge of the detailed structure of the absorption limits. 

Results. These are recorded in tables which give for each element the wave- 
lengths of the different remarkable points in the structure of the discontinuities. 
The theoretical bearing of the new observations is briefly discussed. 

DURING the last few years, an accurate method for determining the 
longer wave-lengths of X-rays has been worked out by M. Sieg- 
bahn and his assistants, employing a vacuum spectrograph designed 
by him.^ An interesting feature of the method is that the wave-length 
differences which can be determined correspond to an amount of energy 
of the order of i volt times the charge on the electron, that is of the same 
order as arises in processes performed in the exterior of the atom. For the 
frequency v, the potential £, and the glancing angle 0, we find 

Av _ AE _ _A0_ 
V ^ E tan ' 

A<^ can be determined by Siegbahn's method and apparatus to within 
io~*. For the longest waves with which one can work, E is about 
i,ooo volts, that is A£ < I volt. It may therefore be expected that 
Siegbahn's method will lead to the detection of many effects which are 
caused by the action of the outermost electrons from which effects a 
calculation of the arrangement of the electrons can be made. For 
instance, it may be found that the position of certain lines of the X-ray 

» M. Siegbahn. Phil. Mag. (37)» P- 6oi. 1919. and Ann. d. Phys. (4), 59. P- S6. 1919. W. 
StenstrOm, Ann. d. Phys. (4). 57. P- 347. 1918 and Diss. Lund., 1919. 



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Na*3^'*] ABSORPTION FREQUENCIES, 203 

spectrum of a given substance depends on the chemical combination 
of the radiating atom. It is also to be expected that the variation in the 
wave-lengths of a given line for the different elements in the periodic 
table will not be continuous, but a little irregular, corresponding to the 
discontinuities in the arrangement of the outermost electrons as we 
progress in the periodic table. Effects of these sorts ought to be most 
strongly pronounced for the limiting frequencies of the series, because 
one of the two energies, on the difference of which the frequency depends, 
is directly associated with the conditions in the outermost part of the 
atom. 

Up to the present time measurements of the longer wave-lengths 
with the precision stated above have been made for only a few lines.^ 

The following is a contribution to the completion of this work. It 
consists of a series of measurements of the limiting frequencies in the 
K-series for the chemical elements from magnesium to chromium. As 
will be seen a rather complex structure of the limit is found. 

The measurements were all performed in 191 8 at the physical laboratory 
of the University of Lund (Sweden), using the vacuum spectrograph of 
M. Siegbahn. It gives me great pleasure to express here my gratitude to 
Prof. M. Siegbahn for putting at my disposal the vacuum spectrograph 
and the other resources of his X-ray laboratory, and for the interest he 
has taken in my work. 

As regards the construction and operation of the vacuum spectrograph 
the reader is referred to the above cited papers of M. Siegbahn and W, 
Stenstrom. 

The method of investigation is that first employed by de Broglie.^ 
A suitable part of the continuous X-ray spectrum from the target in an 
X-ray tube, with an absorbing substance introduced in the path of the 
rays, is photographed. 

Care must be taken to use the proper quantity of absorbing substance. 
Too great or too small a quantity effaces the details of the structure of 
the limit. 

The quantity should be so chosen that the ratio between the intensities 
of the emergent rays on opposite sides of the limiting frequency has a 
convenient value which is neither too great nor too small. 

Glocker* has given two simple formulas, which express the absorption 
coefficient of the X-rays for the two sides of the limit as a function of the 
wave-lengths of the absorbed radiation and the atomic number of the 
absorbing substance. Using these formulae the quantities of the sub- 

* M. de Broglie, C. R., 158, p. 1493. I9i4- 

* docker. Phys. Zeits.. 19, p. 66, 1918. 



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204 BUGO FRICKE, ^SSS 

stances to be investigated were calculated so that the ratio in question 
was about i : 6. 

For most substances the pure element or one of its salts was spread in 
a thin layer upon a thin sheet of paper. This was placed between the 
slit and the crystal. 

Argon was procured from the air by absorption of the oxygen and 
nitrogen. This was done by the well known method of leading the air 
over glowing copper and magnesium. Most of the oxygen was previously 
absorbed by pyrogallol. The argon was drawn at a pressure of 6 cm. of 
mercury into a container. This was made of a brass tube 8 cm. long 
closed at both ends with plates, which, to allow for the passage of the 
X-rays, were provided with slits closed with gold-beater's skin. A test 
before filling the tube showed that it could support a vacuum sufficiently 
well. The tube when under exposure, was placed between the slit and 
the crystal. 

In the case of chlorine, since in this work rock-salt was used as the 
crystal, no particular absorbing substance was needed. 

In the case of aluminium and magnesium some difficulties were en- 
countered, owing to the fact that the absorption of organic substances 
for the long wave-lengths here employed is very considerable. The 
proper quantities of Al and Mg to be used are about 0.25 mg. per cm.* 
(or foils about i /x thick). The most convenient manner of manipulating 
such small quantities would be perhaps to employ the same method as 
is used for most of the other substances (see above), that is to spread 
suitable salts of Mg and Al (Mg O, Alj O3) in a thin layer on a thin 
sheet of paper. As stated in the cited papers of M. Siegbahn and W. 
Stenstr5m, it is necessary to place a suitable foil in the slit in order to 
attain the high vacuum in the discharge tube; the best method for that 
purpose would then be to use gold-beater's skin in the case of Al and a 
thin foil of Al in the case of Mg (the limiting wave-length of Mg being 
longer than the limiting wave-length of Al, its absorption in this substance 
will be comparatively small). This arrangement will, however, owing to 
the great absorption of the gold-beater's skin, and of the paper demand 
too long a time of exjx)sure. For this reason it was decided to employ 
another method. Thin foils of Al and Mg were placed over the slit, 
acting both to seal the tube and to absorb the rays. Owing to the com- 
paratively small absorption of these substances for wave-lengths longer 
than the limiting ones, we can with this arrangement reduce the time of 
exjx)sure very considerably, but in employing this method it is necessary 
to use fairly thick foils, and therefore we will find only the sudden change 
in the absorption. No details of the limit can be found. The Al foil 



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NoTa?^^^*] ABSORPTION FREQUENCIES, 205 

had a thickness of 7 /x, the Mg foil 10 /x. The latter was made from 
ordinary mg. wire by rolling. Foil as thin as 6 /x could be made in this 
way. This thin foil was found, however, to be unable to maintain the 
high vacuum in the X-ray tube, because of small holes which could not 
be avoided at these small thicknesses; nothing thinner than 10 /x was 
found adequate for the purpose. Calculation shows that these two foils 
absorb practically all the radiation of a wave-length smaller than the 
limiting one; in accordance with this, the plates for Mg and Al, as we 
shall see, do not show any structure of the limit. 

The discharge tube is a metal one of the Coolidge type. This is a 
great advantage in this work, owing to the fact that the potential can 
immediately be given the desired value. This is important because 
it is necessary, especially for the longest wave-lengths, to be able to use 
such a low potential that the spectra of higher orders are not produced. 
Otherwise these spectra, their smaller absorption compensating for their 
smaller reflection from the crystal, will be strong enough to mask com- 
pletely the structure of the limit. Care of this must especially be taken 
when working with sugar as a crystal, for here we have a third order 
spectrum which is just as strong as, or even stronger than, the ist order. 
An unpleasant consequence of the low potential is the comparatively 
slight intensity of the radiation. For the lightest substances the low 
jx)tential causes further difficulty, in that here the space charge prevents 
the passage through the tube of the great current usually used, and par- 
ticularly desirable in this case. For magnesium-, in order to obtain a 
current of the proper magnitude, it was necessary to use a potential 
rather greater than that indicated by the above-mentioned considerations; 
in consequence we have here a distinct superposition of the third order 
spectrum (see below). Tungsten was used for the anticathode. It gives 
a very strong continuous radiation, and allows the passage of a large 
current. The same metal was used for the incandescent spirals. The 
current through the tube was about 40 milliamperes, the time of exposure 
varying from 3 to 16 hours. Only one plate of each substance was 
taken; in order to get the right time of exjx)sure at once, a rough calcula- 
tion of the absorption of the wave-length in question was made before 
the exposure, and the time for this chosen in accordance with the result 
obtained. So far as possible the chemical compound of the absorbing 
substance was chosen so as to contain only very light atoms. This, 
however, was not always possible. 

A sugar crystal was used for the lighter substances examined. For 
the others a rock salt crystal was employed. The reflecting power of 
both these crystals is very good. The grating constant used for sugar is 



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206 HUGO FRICKE. ^ms. 

log 2d = 1.32503 
and for rock salt 

log 2d = 0.750354, 

The first was determined by photographing the CuK« line using for the 
wave-length of this line the value given by Siegbahn.^ The second is 
the generally adopted value. 

The width of the slit (between the anticathode and the crystal) was 
o.io mm. 

Under exjx)sure the crystal was turned through a certain angle so that 
a proper wave-length interval around the wave-length in question is 
obtained on the plate; this angle was 1^.5-2.^0. 

For the calculation of the desired wave-lengths from the photographic 
plate, it is necessary to photograph a known spectral line on the same 
plate. For this purpose lines only are used on which precision measure- 
ments had already been made at Lund.^ 

To determine the different details in the limit a photometric investiga- 
tion of the plates was made. The arrangement used for this was the 
following: Through a microscope objective a narrow ray of light (.02 
mm. wide) from an incandescent lamp run by a storage battery, was 
thrown on the plate; after emerging it was suitably enlarged and thrown 
upon a thermopile; the deflection of a galvanometer connected to this 
gave a measure of the blackening of the plate. The plate was mounted 
on a slide; the galvanometer mirror formed an image of the filament of 
an incandescent lamp upon a photographic paper wrapped around a 
cylinder. Automatic registration could then be obtained by coupling 
(by toothed wheels) the cylinder and the slide. The slide was moved' 
by a motor at a speed determined by the oscillation constants of the 
aperiodic system composed of the thermopile and the galvanometer. 
These constants were previously determined by a simple experiment. 

The ratio between the distances on the plate and on the photographic 
paper must be determined for each plate, as the dimensions of the paper 
are altered slightly when it is developed. For this purjx)se, before the 
photometric investigation, two fine lines are drawn on each plate at a 
convenient distance from the limit. They are recorded very distinctly 
on the curve of blackening. By measuring their distance on this and on 
the plate the desired ratio can be obtained, and is found to be about 
17.46 : I. The measurement on the plate was made with a comparator 
with better than .01 mm. accuracy. 

By means of a microscope the correct orientation of the light ray on 

» M. Siegbahn. loc. cit. 
« M. Siegbahn. loc. cit. 



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Na*3?^^''J ABSORPTION FREQUENCIES. 20/ 

the plate is obtained. Owing to the short length (i mm.) of the ray 
three investigations are made, with the ray at the upper, middle and 
lower part of the plate. 

Only the part of the plate around the limit is investigated ; the distance 
of the reference line from one of the drawn lines is measured with the 
comparator with an accuracy of about .01 mm. 

By the photometric method here described the jx)sition of the points 
on the photographic plates can be determined with an accuracy of a few 
hundredths of a mm. A difficulty encountered in this method is the 
above mentioned alteration of the photographic paper when developed; 
this is not always exactly the same in every part. 

No limit was found for silicon. First a plate was taken with the 
above mentioned arrangement. As absorbing substance pure silicon 
was used, spread in a layer of .70 mg. per cm.^ on a sheet of paper. Dur- 
ing the exjx)sure the crystal was turned through an angle corresponding 
to the wave-length interval 

X = 6.46 - 7.09A (Si K^iX = 6.76).^ 

No limit could be detected on the plate. The reason may be that the 
limit was covered by the WM^u line; this has a wave-length of 6.75 A, 
and is recorded very strongly on the plate. 

A new plate was taken with platinum as anticathode; this time / 
used 1.7 mg. of silicon per cm.^ and examined the wave-length interval 
X = 6.35-7 .09A. No limit could be detected; still the WM^i line was 
rather strong owing to the deposition of tungsten from the incandescent 
spiral on the target. Later, spirals of molybdenum were tried. These 
were found to be impracticable because of their great evajx)ration, which 
causes so poor a vacuum that a sufficiently strong current could not be 
obtained, and also causes the spiral to be rapidly consumed. Tantalum, 
which probably would have been found very suitable, was unfortunately 
not procurable. 

As has already been mentioned above, the plates show that the limit 
is not, as has been commonly thought up to this time, a simple dis- 
continuity in the blackening of the plate, which covers a wave-length 
interval equal to about the width of a spectralline; but it is found, that 
the limit presents a rather complex structure. As a rule we can state: 
we have on the plate two parts of uniform, but unequal blackenings; 
the limit is the transition between these two; the stronger of the two 
blackenings has always on the side of the shorter wave-lengths a very 
distinct boundary (Km), on the other side of this we have a very bright 

* M. Siegbahn and W. StenstrOm, Phys. Zeits., 15, 1916. 



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208 HUGO FRICKE. [^S? 

line or band (L) ; after this we frequently have a dark line and then again 
sometimes a bright band. 

On the plates for chromium, vanadium and titanium, a characteristic 
narrow dark line is seen in the bright line L close up to the boundary Km; 
the phenomenon is most pronounced for chromium and vanadium; for 
titanium the fine bright boundary line between Km and the dark line 
is less distinct. 

No structure is found for the limits of magnesium, aluminium and 
argon. As regards the first two substances, this was to be expected 
for the reason mentioned above. As regards argon the reason perhaps 
may be that the plate is rather underexjx)sed. 

In the following for each substance tables will be given containing the 

wave-length (X, unit A) of Km and the wave-length difference (AX, 

unit A) between Km and the diflferent remarkable points in the structure 

of the limit, also the distances (Ax unit mm.) on the photographic plate, 

the frequency differences (Av unit : lo^^) and energy differences (Ae unit: 

volt times the charge of the electron) corresponding to the fatter are given. 

AX is determined by: 

X 

AX = — Ax, 

27 tan fp 

X : Wave-length of Km, 

(p : glancing angle, 

y : Distance from the axis of the vacuum spectrograph to the photo- 
graphic plate. In addition a description of each plate is given. Owing 
to different well known optical illusions, it is always specially emphasized 
when features observed in the plates are not shown in the photometric 
curves. 

12 Magnesium (Fig. i). 

Absorbing screen: pure Mg: 1.74 mg. per cm.^; reference line: 

SnLai X = 3-5929- 
Crystal: Sugar. 
Spectrum — ist order. 

K,„ :X = 9-5112 A., 
Km — Ki : A.r = 0.26 mm., 
AX = 0.019 A., 
Av = 0.64 X .io*\ 
At = 2.7 volt. 

Description of the plate: No structure of the limit is seen; this appears 
only as a distinct discontinuity Km — K^ in the blackening of the plate. 



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Vol. XVI.1 
.3. J 



No.; 



ABSORPTION FREQUENCIES, 



209 



13 Aluminium (Fig. i). 

Absorbing screen: pure Al, 1.89 mg. per cm.*; reference line: 

WLai : X = 14735 ^^^ SnLai : X = 3.5929. 
Crystal: Sugar. 
Spectrum: ist order. 

Km : X = 7-9470 A., 

Km — K/ : Ajc = 0.32 mm., 
AX = 0.025 A., 
Av = 1. 18 X lo^*, 
A€ = 4.9 volt. 

Description of the plate: What is stated for magnesium will apply here 
also. 

15 Phosphorus (Fig. 2). 

Absorbing screen: HjPOa, 0.80 mg. P per cm.*; reference line: 

Sn -fai X = 3-5929- 
Crystal: Sugar. 

Spectrum: 3d order. 

Km : X = 57580 A. 



Ax. 

AX. 
Ay. 

Ac. 



K^-^S.. 



0.52 mm. 
0.0084 A. 
0.76.10" 
3.16 volt 



Km — K{. 



0.86 mm. 
0.0139 A. 
1.26.10" 
5.25 volt 



Description of the plate: Two parts of unequal blackening (I — K„ 
and Kj — n), separated by a bright line (K^XKi). 



16 Sulphur (Fig. 3 and Fig. 9). 
Absorbing screen: S, 0.90 mg. per cm.*; reference line: 

Sn-fofi X = 3-5929- 



Crystal: , 
Spectrum 


Sugar. 

; 3d order. 

Km 


:X 


= 5.0123 A. 






K„-5.. 




1 J^-Sftl. 


Km-N. 


Ax 

AX 

A^ 

Ac 


0.23 mm. 

0.0045 A. 
0.54.10" 
2.3 volt 




0.64 
0.0125 
1.49 
6.2 


1.29 
0.0253 
3.02 
12.6 



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2IO 



HUGO FRICKE, 



rSBCCNtD 

LSsmiBs. 



Description of the plate: Starting from the boundary " (K,„) of the 
stronger uniform blackening (I — K,h), we have first a distinct bright line 
{KntXdU^ 0.3 mm.), then a distinct dark line {3U) and then at last a very 
faint bright band (MN, 0.7 mm.), which, with an apparently distinct 
limit, borders on the fainter uniform blackening (N — n). 

Whether there is in reality a distinct limit between the bright band 
(MN) and the uniform blackening (Nil) cannot, owing to the faintness 
of the bright band, be decided with certainty from the photometric curves. 



No absorbing screen. 
Crystal: Rocksalt. 
Spectrum: ist order. 



17 Chlorine [Fig. 3]. 
Reference line: ClKai X = 4.7187. 

Km = 4-3844- 





K«-S.. 


K^-S^. 


Ay 


0.43 mm. 
0.0060 A. 
0.93. 10i» 


0.95- 


AX 


0.0132 — 


Ay 


2 06 — 


A€ 


3.9 volt 


«.6- 



Description of the plate: Looks exactly like that for sulphur; the bright 
line apparently is 0.6 mm., the bright band 0.9 mm. wide. 

18 Argon (Fig. i). 

Absorbing substance: A., 1.5 mg. per cm.^; reference line: . 

Sn iixi X = 35929- 
Crystal: Sugar. 
Spectrum: 3d order. 

K« X = 3.8657. 

Ajc 0/14 mm. 

AX 0.0033 A. 

Ar 0.67.10" 

Atf 2.8 volt. 

Description of the plate: The same as for those of magnesium and 
aluminium. 

19 Potassium (Fig. 4). 

Absorbing substance: K2CO8, 2.00 mg. K per cm.^; reference line: 

SnXa : X = 3.5929. 
Crystal: Sugar. 



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Vol. XVI.l 
No. 3. J 



ABSORPTION FREQUENCIES. 



211 



Spectrum: ist order. 





K^:X = 


'' 34345. 






J^-L. 


J^-sn. 


J^-L\ 


Ay 


0.16 mm. 
0.013 A. 
3.4.10»» 
14. volt 


0.35- 
0.027- 
6.9- 
29.- 


0.47- 


AX 


0.039- 


Ay 


9.9- 


Ac 


41.- 



Description of the plate: Looks about the same as the plates for sulphur 
and chlorine; a bright line (-Q, a dark line (M) and a fainter bright band 
(^); no distinct limit of this however can be seen here; still it must be 
remarked, that, SnJ^fiy which is presented very strongly, perhaps covers 
the last part of the bright band. 

The photometric curves seem to indicate the same structure for the 
bright band as for the bright line -T. 

20 Calcium (Fig, 2). 
Absorbing substance: CaCOs, i mg. Ca. per cm.*; reference line: 

CuKai X = 1.5374. 

w^i X = 1.4735. 

Crystal: Rocksalt. 
Spectrum: ist order. 

K« : X = 3.0633 A. 



1 K^-A 


K.-K,. 


Ay 


0.41 mm. 
0.0078 A. 
2.48.10»» 
10.3 volt 


1.2- 


AX 


0.023- 


Ay 


7.4- 


At 


31 - 



Description of the plate: Looks about the same as the plate for phos- 
phorus. 

21 Scandium (Fig. 5.) 

Absorbing substance: Sc2(S04)8f 1.7 mg. Sc. per cm.*; reference line: 

VKai X = 2.4987 A. 
Crystal: Rocksalt. 
Spectrum: 1st order. 

K,n : X = 2.7517 A. 



K«-il. 



K^-M. 



K^-N. 



Ax. 
AX. 

Ac. 



0.47 mm. 
0.0091 A. 
3.62. 10i» 
15.1 volt 



1.14- 
0.0222— 
8.79- 
36.7- 



2.30- 

0.0446— 
17.67- 
73.7- 



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212 



HUGO FRICKE, 



rSscoND 

ISBftlBS. 



Description of the plate: Here and also on the following plates for 
titanium and vanadium two dark, rather broad and diffuse lines (Mi 
and Mj) are seen in the fainter uniform blackening; their distances from 
Km are about l and 3 mm. ; the first is the stronger; it forms the boundary 
between J^ and the fainter uniform blackening. The existence of the 
second is perhaps questionable; it cannot be shown with certainty on 
the photometric curves. 

22 Titanium (Fig. 6 and Fig. 10.) 
Absorbing substance: Ti02, 2.0 mg. Ti per cm.*; reference line: 

Cr Kai X = 2.2852. 



Crystal: Rocksalt. 
Spectrum: ist order. 



K,h' , X = 2.4937. 



Ax 

AX 
Ac. 



K^-^V 



[K^-S."]. 



0.63 mm. 
0.0124 A. 
6.0.10»» 
25.0 volt 



1.07- 

0.0214- 
10.3- 
43.0- 



K^-m. 



0.14- 
0.0028- 
1.3- 
5.6- 



Description of the plate: Mi (see under scandium) has here a very 
distinct boundary on the side toward the bright line J^; this has a very 
well defined breadth (J? — -^0- In the middle of -T is seen a very faint 
dark line M'; where this is shown on the photometric curves cannot with 
certainty be determined. As already mentioned above we have a very 
dark distinct line (here not so pronounced as in the case of vanadium 
and chromium) in -T close up to K^; it is shown in the photometric 
curves at m. 

23 Vanadium (Fig. 7). 

Absorbing substance: VeOs, 2mg. V per cm.^; reference line: 

Fe Kai : X = 1.9324. 
Crsytal: Rocksalt. 
Spectrum: ist order. 

Km : X = 2.2653. 





K^-1. 


K^-m. 


K^-il. 


K^-M'. 


K^-M. 


Ax 

AX 


0.17 mm. 
0.0035 A. 
2.0.10" 
8.5 volt 


0.26- 
0.0053- 
3.1- 
^2.9- 


0.60- 
0.0123- 
7.2- 
30.0- 


1.18- 
0.0242- 

14.2- 

59.0- 


1 1.60- 
' 0.0327- 


Ay 

A« 


19.1- 
1 79.8- 



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Physical Review. Vol. XVI., Second Series. 
September. 1920. 



Plate I. 
To face page 212. 




Fig. 1. 

Aluminium. 



Fig. 2. 
Phosphorus. 



I K^ M 

Fig. 3. 
Sulphur 



I II 



ml- 

Fig. 4. 
Potassium. 



Fig. 5. 
Scandium. 



Fig. 6. 
Titanium. 



1. 1\\^ ilJV 



Fig. 7. 
Vanadium. 



Fig. 8. 
Chromium. 



Fig. 9. 
Sulphur. 



HUGO FRICKE, 



Fig. 10. 
Titanium. 



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Na*3?^^'] ABSORPTION FREQUENCIES. 2I3 

Description of the plate: Like the plate for titanium ; the dark line m 
close to K,„ is here seen very distinctly; the bright line between m and 
Km is shown on the photometric curves by 1. 

24 Chromium (Fig. 8). 
Absorbing substance: K2Cr04, i mg. Cr. per cm.^; reference line: 

W^iX = 14735- 



Crystal: Rocksalt. 
Spectrum: ist order. 


K^:X = 


'- 2.0675 A. 






1 K« - 1. 


K^-m. 


K^'L. 


K« - M'. 


K«-M. 


Ax 

AX 

Au 

A« 


0.13 mm. 
0.0026 A. 
1.8.10" 
7.6 volt 


0.20- 
0.0040- 
2.8- 
11.8- 


0.47- 
0.0098- 
6.8- 
28.6- 


0.74- 
0.0153- 

10.7- 

45.0- 


1.05- 
0.0218- 

15.3- 

64.0- 



Description of the plate: The two dark lines Mi and M2 are not seen 
here; the bright line -f has very distinct boundaries on both sides (J? 
and -i^O ; as in the case of titanium and vanadium a very faint dark 
line M' is seen in the middle of -T. What is stated for vanadium about 
the dark line m will apply here also. 

No satisfactory theory for the limiting frequency has as yet been 
published. Kossel/ on the basis of Bohr's theory, regards the limiting 
frequency of a certain series as corresponding to the passing of the electron 
from the ring in the atom, corresponding to this series, to the space out- 
side all the rings of electrons in the atom. On the basis of this theory, 
a theory for the structure of the limit here discovered would be, that 
different orbits exist outside the atom, to all of which the electron (with 
different probabilities) can go starting from the K-ring. The different 
passages corresponding to these orbits will give a series of absorption 
lines. Further, the electron from the K-ring can pass to infinity with 
all kinds of velocities (still with a varying probability) ; this will give a 
broad absorption band succeeding the above-mentioned absorption lines. 
The last type of passage is used by Bohr^ to explain the continuous 
absorption band, which is observed by R. W. Wood at the head of the 
principal series of sodium, extending to the extreme ultra-violet. 

It ought, however, to be mentioned that this theory does not seem to 
explain the more special formation of the structure observed for the dif- 
ferent substances. 

» W. Kossel. Verh. d. D. Phys. Ges. (i6). p. 953, 1914. 
*N. Bohr, Phil. Mag. (26). p. 17, 1913. 



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214 



hugo fricke. 
Table for K... 



rSacoMD 

LSBRICt. 



Atomic 
Number. 


Element. 


K.:x. 


>if 


Difference. 


12 


Mg 


9.5112 


0.32425 


.3050 


13 


Al 


7.9470 


0.35475 




14 


Si 






(.6199) 






15 


P 


5.7580 


0.41674 


.2992 


16 


S 


5.0123 


0.44666 


.3093 


17 


CI 


4.3844 


0.47759 


.3102 


18 


A 


3.8657 


0.50861 


.3099 


19 


K 


3.4345 


0.53960 


.3175 


20 


Ca 


3.0633 


0.57135 


.3149 


21 


Sc 


2.7517 


0.60284 


.3042 


22 


Ti 


2.4937 


0.63326 


.3116 


23 


V 


2.2653 


0.66442 


.3105 


24 


Cr. 


2.0675 


0.69547 





For none of the substances, with the exception of Mg, are the wave- 
lengths of the limit found, with certainty, longer than any of the K- 
lines. For Mg the wave-length in question is found considerably longer 
than the wave-length of the K^i line.^ The reason for this perhaps may 
be illustrated by the following simple consideration : The K^ line corre- 
sponds to a transmission of the electron from one ring of electrons (the 
M-ring) to another ring situated nearer the nucleus (the K-ring). A 
simple calculation shows however, that more energy is not always 
required to move the electron from the innermost ring to infinity than 
to move it between two such rings. The latter passage can require the 
greater amount of energy if the M-ring is situated in the exterior of the 
atom. 

Limiting frequencies have previously been determined by de Broglie,^ 
Wagner^ and Siegbahn-Jonsson* using the photographic method and by 

» M. Siegbahn and W. Stenstr6m, loc. cit. 

» M. de Broglie, C. R., 163, p. 87, 1916, and Jour, de Phys., 5. p. 161, 1916. 

• E. Wagner. Bayr. Akad. d. Wiss., 1916. 

* M. Siegbahn and E. Jonsson, Phys. Zeits., 20, p. 251, 1919. 



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nS"3^^^*1 absorption frequencies, 215 

Blake^-Duane, Duane^-Kang-Fuh-Hu and Duane-Takeo Shimizu* using 
the ionization method/ 

No structure of the limit has been found by any of these authors. As 
regards the smaller wave-lengths the reason for that is certainly that the 
structure here covers so small an interval of wave-length, that it could 
not be observed with the accuracy obtainable in the investigations con- 
cerned; this agrees with the theory here given. As regards the longer 
wave-lengths, the reason may be that in order to get sufficiently high 
intensity and a distinct limit the investigators have used comparatively 
broad slits, high potentials and large quantities of the absorbing sub- 
stances.^ 

Copenhagen, Denmark. 

* F. C. Blake and W. Duane. Phys. Rev., 10, p. 697, 191 7. 

« W. Duane and Kang-Fuh-Hu, Phys. Rev., 14, p. 516, 1919. 

* W. Duane and Takeo Shimizu, Phys. Rev., 14. p. 52a, 1919. 

* After the completion of this work, W. Stenstr6m (Diss. Lund. Sweden 1919), using: 
the photographic method, has found three limits in the M-series. These present a structure 
about the same as is found here; however, the whole complex is, as to be expected, rather faint. 

* Wagner* states, that in his investigation of the limit of Iron he has used a foil of Iron o.oa 
mm. thick. A calculation shows that this foil will absorb practically the whole radiation of 
shorter wave-lengths than the limiting wave-length. Furthermore he has used a slit 0.4: 
mm. wide. 



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2l6 R. A. HEISING. ^ISJ^ 



THE AUDION OSCILLATOR. 

By R. a. Hbising. 

Synopsis. 
Conditions Bordering Free Oscillations in Audion Generator Circuits. — Conditions 
required for the production of free oscillations in audion oscillator circuits can be 
mathematically predetermined. It necessitates an assumption of a straight line 
-characteristic for the tube, which assumption becomes exact for small oscillations. 
The required conditions can be expressed in terms of the constants of the circuit 
elements and the constants of the tube. The equations are set up as for ordinary 
<:ircuits making use of Nichols' explanation of the behavior of the audion in which 
the amplifying action is ascribed to a fictitious generator located between the plate 
and filament inside the tube and having a voltage m times the voltage applied to the 
grid. Two simple circuits are treated in detail and results plotted in several sets 
of curves. 

I. Introduction. 

THE audion generator of sustained high frequency currents has been 
the subject of much investigation during the past few years and 
has given rise to numerous papers. It has been discussed by Hazeltine 
(I.R.E., April, 1918), Vallauri (L'Elettrotecnica, January, 1917), and 
in Bureau of Standards Circular No. 74. The writer has done consider- 
able work along this line, both theoretical and experimental, and many 
of the results are in the course of publication. Analytic studies have 
been made by Hazeltine, Vallauri and others. In this article duplication 
of their work will be avoided where possible. 

2. Approximations and Assumptions. 
The difficulty of securing an exact solution for audion circuits has 
been evident to all investigators. The primary reason is found in the 
nature of its characteristic curve. According to Van der Bijl, the equa- 
tion expressing its behavior is 

i = B{E, + nE, + k)\ (I) 

where £& is the plate potential, Ec is the grid potential, /x is the amplifica- 
tion constant and B and k are constants. This curve is a parabola 
which makes any circuit equations derived from it extremely complex. 
Vallauri assumes a straight line characteristic at the outset as does 
Hazeltine by his definition of mutual conductance g. The straight line 
equation will be assumed in this work for several reasons. They are: 



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No!* 3?^^^*] ^^^ AUDION OSCILLATOR, 217 

(i) the solution is simplified (2) according to Van der Bijl (Phys. Rev., 
Sept., 1918, p. 182) the output impedance of the audion is independent 
of a variable potential impressed on the grid (3) the above parabolic 
equation ceases to hold when Eb becomes negative, Ee becomes positive, 
or Eb + fiEc + * is negative. From the second reason we deduce that 
the equations derived hold not only for small oscillations over such a 
small part of the curve that it is sensibly a straight line, but they hold 
for large oscillations up to the value that will make Eb negative, £<, 
positive or Eb + fiEe + k negative. Under these conditions (reason 3) 
equation i is no longfer the charac- 
teristic curve as the latter takes the 
form shown by the full line in Fig. i. 
The parabolic equation fits the actual 
curve over only part of its length. 
For positive values of £« two things 
occur in the tube which are not con- 
tained in this equation — (a) current 
flows from the grid to the filament, p. - 

(b) voltage saturation of the filament characteristic curve. 

occurs. These things cause the actual 

curve to depart from the right-hand limb of the parabola as shown in 
Fig. I. For negative values of Eb + fiEc + k the left-hand limb of the 
parabola disappears entirely. For negative values of Eb regardless of 
the value of Eb + fiEe + k the equation fails. These departures make 
it useless to consider the parabolic equation in any oscillator solution. 
The actual function containing all variables is exceedingly complicated. 

The assumption of the straight line equation together with reason 2 
give equations which hold for the oscillation frequency up to the limits 
mentioned and give circuit conditions required for oscillating as well as 
most of the transient conditions correctly. 

3. Equation Assumed. 
The equation assumed is 

i = B{Eb + nEc + k). (2) 

The output impedance (or internal impedance as it is sometimes called) is 

^ di B ^3; 

and is constant at all times. In setting up the differential equations of 
the circuit advantage is taken of the theorem stated by Nichols in the 



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2l8 R. A. H EI SING. 

Physical Review, Aug., 1917, that an element whose impedance value 
varies can be considered as having a constant value but with a variable 
E.M.F. located within. In the case of the audion, the constant resistance 
is the output impedance Z in equation (3) and the contained E.M.F. 
is M-Ec Referring to Fig. 3, which is a diagrammatic representation of 
Fig. 2, the fictitious generator G is located within the audion and has 





St 

Fig. 2. Fig. 3. 

Hartley oscillator circuit. Electrical equivalent of Hartley circuit. 

an E.M.F. /xe, where e is the E.M.F. across Li (between grid and filament). 
If instead we set up the differential equations in the regular manner and 
substitute equation (2) identical results are secured. For simplicity 
and clearness, Nichols' method is the better. 

4. The Oscillatory Circuit. 
The simplest tyoe of oscillatory circuit consists of an inductance, a 
resistance, and a capacity in series. The differential equation of the 
circuit is 

di Cidt 

^5-/ + ^» + Jt = ^' (4) 

where E is constant. The solution of this circuit is secured by making 
the assumption that 

i = Ae'K (5) 

Differentiating (4) and substituting (5) 



YLa» + i?o + ^) = 



Ae" ( La' + i?o + 7; I = o. (6) 



Solving for (a) 



R [^ T 

Giving as the solution 

i = Ae^ '^^ *^* '-^f + Be^ ^^ ^^* ''^' . (8) 

The values of A and B are secured by substituting the boundary condi- 
tions in a given case. The part with which we are concerned, however, 



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Na'a^^'J ^^^ AUDION OSCILLATOR. 2I9 

is the exponential constant a. Under certain conditions, viz: {IP/4D) 

< (i/LC) the radical term is imaginary. The exponential term then 

has the general form 

R , 
a = - ^ =b jco, (9) 

which means that the circuit is oscillatory, that the frequency of oscilla- 
tion is a)/27r, and that the o scillations are dam ped according to e^~^^^^ 
The value of w is given by V(i/LC) — (iP/4L*) and is largely dependent 
upon the inductance and capacity. 

The length of time the oscillations last depends upon the vlaue of 
— {R/2L), If this is large numerically, the oscillations die out rapidly; 
if it is very small, the oscillations will continue for a considerable time. 
If we can make it zero, the damping term e^'^^^^ reduces to unity for 
all values of time, and we have the condition of oscillations occurring 
without a driving E.M.F. which oscillations neither increase nor decrease 
with time. If, however, we can make the exponent positive, the damping 
term becomes an ''undamping" term e^'^'^^^^', and the oscillations will 
increase with time. If we insert a carbon arc in a series circuit containing 
inductance, capacity and low resistance, the combination produces the 
condition just referred to — a positive damping constant — and oscillations 
occur which increase with time. Such oscillations once started increase 
continuously until some characteristic of the arc or circuit is altered. 
The alteration occurring reduces the damping constant to zero after 
which the oscillations continue indefinitely with unchanged amplitude. 

5. Production of Oscillations by an Amplifier and its Circuit. 
Continuous oscillations can also be produced by amplifiers. An am- 
plifier is a device which takes power in some form but converts part 
of it into a different form due to the operation of a control member. 
A relay is an amplifier. The magnet is the control member and the 
power conversion occurs by the making and breaking of the armature 
contact points. A relay provided with a spring, bell, and clapper forms 
an electric bell and can be used to produce oscillations. The bell takes 
power in the form of unidirectional current and converts it into mechan- 
ical and electrical oscillations by virtue of the control elements (magnets) 
operating on the armature and varying the electrical constants in some 
part of the circuit (breaks a contact). The audion acts in a similar 
manner and produces oscillations. Potential changes on the grid (instead 
of current through a magnet) cause the plate to filament resistance to 
change and power is delivered to a circuit. Equation for systems like 
these are discussed by Nichols (Physical Review, August, 191 7) and 



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220 R. A, HEISING, [^Sw? 

are solved in* the same general manner as are those for the simple cases 
mentioned previously. 

6. Circuit Equations. 

The simpler oscillator circuits only will be considered. The more 
complex circuits can be more clearly explained by applying to them the 
deductions made from the simple circuits than can be done by using the 
complicated equations of the complex circuits themselves. The circuit 
shown in Fig. 2, called the Hartley circuit on account of its inventor, is 
shown diagrammatically in Fig. 3. The equations, assuming the current 
directions indicated by the arrows as positive, are 

di\ di± r i\dt 

(dii dii \ 

R,i, + L,-^-M-^), (10) 

dt\ dtA ( d%\ diix 

The right-hand terms stand for the voltage generated by the fictitious 
generator G, The voltage is opposite in direction to the drop across the 
inductance Li and is therefore given an opposite sign. M is the mutual 
inductance between Li and Li. In these equations, the continuous 
potentials and currents are omitted as they cancel out. The equations 
stand for the varying values only. 

The assumption is now made that the current in any part, such as in 
Li has the form (as in equation 5) 

ii = /i«*'. (11) 

On substituting in the above equations and dividing out the «•' term 
we have 

Ii{Ri + all) + I, (i?5 + ^)+ IiRz - UMa + I,Rz 

= - ii{h{Ri + aLi) - UMa,) (12) 

"hMa+hRz+IiRz+hiRi+aU) = -tiihiRi + aLi) - UMa), 

If the exponent a is a pure imaginary number such as jw, the equations 
reduce to the usual complex form for alternating current circuits. We 
are then justified in writing in a more simple manner the above as 

/i(Zi +Z, + Zn + M^i) + UZ, - ty - mWO = 0,1 
I,{Zz -^W + ixZi) + U{Zz + Z4 - nW) = O.J ^^ 

Where Zi, Z6, etc., are the complex impedances of the circuit elements. 



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Nc^a^^^'l ^^^ AUDION OSCILLATOR. 221 

Heaviside (Electrical Papers) and Campbell (A. I. E. E., Apr., 191 1) 
have shown that such equations also hold where a is complex — that is 
with damped or expanding oscillations. Equations 13 thus hold for 
any value of a and in this case the impedances are: 

Zi = Ri-\- aLu 
Z4 = Ri + gLa, 

I 



Zz = i?8. 



(14) 



These are the values for the particular circuit considered (Fig. 2) but 
can be given different values if the elements of the oscillator are con- 
structed in other ways than that shown. 
On solving this equation for /i we get 

This equation has the dimensions of a zero E.M.F. divided by an im- 
pedance of the value 

(Z,+Z,-nW)(Zi+^i+Z,+Z,)-(Zt-W-^W){Zt+nZr-W) . ^. 

wTY, ^'^^ 

and giving a finite current. Such a condition obtains only if the im- 
pedance is also zero. We can thus write the determining equation for 
free oscillation 

(Z, + Z4 - nW){Zt + imZ, + Zz + Z5) 

- (Z3 - PF - mW0(23 + mZi - wo = o. (17) 

This equation tells nothing about the value of /i. It indicates only 
the conditions obtaining under which a current can flow without an 
applied E.M.F. It is the usual equation giving the frequency and damp- 
ing constants of transient currents in a circuit. In this type of circuit, 
however, the transients may not be damped, but may expand. The 
equation determines the value of the exponent a in equation 11, just as 
equation 6 gives its value for the ordinary oscillatory circuit. The 
actual value of /i is determined by the boundary conditions imposed by 
the oscillator circuit when the switch is closed, and the logarithmic 
term e*' as affected by the value of a and the lapse of time /. 

In the actual circuit, the latter mentioned increase of current with 
time does not continue indefinitely due to the limitations of the audion 
characteristics and the steady state conditions resulting cannot be deter- 
mined by these equations. 



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222 



R. A, H EI SING. 



rsscoMD 
ISbkiss. 



On collecting the terms in a different way 

ZaCZi + Z4 + Z5 + 2TD + (m + i)(ZiZ4 - W^ - Z,W) + Z,W 

+ Z4Z5 = o. (18) 

This equation holds for any circuit having impedance in the places of 
Lu La or C. For applying it to them it is only necessary to substitute 
their impedances in a form similar to those in equations 14. 
For the Hartley circuit substitute (14) in (18) 

ZaTi?! + i?4 + i?6 + aLi +aL4 +^+ 2aJlf J 

+ (m+i) \ RiRi+a^LiLA+aRiU+aRALi-a^M^-aMR^- ^1 



+ aMR, + ^+ i?^5 +^* + ^+ aRJL, = o. 



(19) 



Multiplying through by a and collecting in terms of its descending powers 

a\ii + i)[LiL, - Jlf»] + an2»(Li + L* + 2M) + (m + i){RxL^ 
+ RJ.I - MRi) - MR, + Ra^4\ 

+ a ^Z»{Ri + Ri + R,) + (m + I) ( RiRi - ^)+ R4R, 
^M^Ln^Z, + R, 



which has the general form 

a* + a^x + ay + z — o, 
where 



(20) 
(21) 



X = 



Z,{Li+L4+2M)+{n+i){RtL,+RJ.i-MR,)+Ri{L,-M ) 
Z»{Ri+R,+R,)+{l^+i) (^RiRa- ^) 



+R^.+^^ 



i^+i){LxL,-AP) 



z = 



Zi+R4. 



(22) 



An equation of this type has three roots. If these roots are P\, Pj 
and Pt the coefficients in the equation are: 

X = - (Pi + Pj + P»), 

y = P1P2 + PiP» + P»Pi, |- (23) 

Z = - PiPiPt. 



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No. 3. J 



THE AUDION OSCILLATOR. 



223 



As we are expecting a solution giving a freely oscillatory condition, 
we know that a is complex and that the above coefficients are all real. 
The roots must have the form 



-Pi = <ii + j«, 
to satisfy these conditions. Combining with (23) we get 



(24) 



JC = — dj — 2du 

y ^ di^ + 0}^ + 2didi, 



(25) 



where di and dj are the damping constants and « = 2t/. 

As stated before, if di is zero, the oscillations when once started will 
persist indefinitely, neither decreasing nor increasing. If di is negative, 
they will, as in all ordinary tuned circuits, die out. The condition under 
which a circuit will just oscillate is that of di = o but if it is the slightest 
bit greater, oscillations will increase with time. The condition of most 
interest to us is that condition of the circuit at which oscillations just 
will, or will not occur as we are then enabled to determine the circuit 
requirements under which free oscillations will, or will not take place. 
It marks the change from the normal stable circuit to the freely oscilla- 
tory circuit and the conditions of the circuit influencing this change are 
of the utmost importance. 

The equation (21) as it is, admits of no simple exact solution accurate 
under all conditions but does admit of an exact solution at and near the 
condition of di = o. If we take the case of di almost zero, we can neglect 
it in comparison with dj or w in equations (25). If we do not consider it 
exactly zero, the term containing the product of di and dt must be left 
in, and it enables us to determine the value of di at and around zero with 
extreme accuracy. Under this condition we can rewrite equations (25) 
neglecting the second powers of di and the first power in comparison with 
di giving 



X ^ - di, 

y = w2 + 2did2, 

2 = — diixl^f 



from which 



^2= - 
X 



X, 



-i'-y)- 

2x\x ■'J 



(26) 



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224 ^- ^- SEISING. ^Sw. 

7. Direct Current Transient Term. 
From equations 22 and 26 we can write 

. _ Z,{Li+L,+2M) + (fJ^+i)(RiL4+RiLi-MR,)+R,{L4-M) 
^'■■" (M+i)(L,L4-i/^) ' • ^^^^ 

This factor is always negative under conditions even approximating 
those of free oscillation and indicates that the current term multiplied 
by e*'*' decreases with time under all conditions in the circuit. It is the 
space current damping term. This transient term is not of much im- 
portance to us as it multiplies no periodic or A.C. term and therefore 
is not concerned with the oscillation current in the circuit but can only 
be concerned with a direct current term. It indicates the rapidity with 
which the space current builds up to its final value. If we consider 
Ru Rif and R^ as zero, Cs as infinite and M as zero, and look at the circuit 
as a resistance Zz in series with two parallel inductances Li and L4 this 
damping term reduces to 

Zz 

(m + I) 



Li + L, 

In this, {LiL^I{Li + L4) is the effective inductance of the two induc- 
tances in parallel. If /n = o which is the case of a pure resistance for Zz 
with no amplifying characteristic, the equation is 

^2= "2;^, (29) 

where L« is the effective inductance and Zz is the resistance. This is the 
damping constant in a circuit containing only inductance and resistance. 
The direct current solution for this circuit is therefore, 

Eh + tiEc + * , d^s / X 

t = Z^J^R^ (^ " ^ )» (30) 

where Ec is whatever constant negative potential is applied to the grid, K 
is a constant and d^ is the value given in equation 27. It will be observed 
that if M is large, the damping constant d^ is small, and that it will take 
a longer time for the space current to rise to the final value than in the 
case of a low m audion. 

8. Frequency Term. 
From equations 22 and 26 we get the frequency term 

Zz+Rj 
" C{n+l){LrU''m 

y (m+i)(LiL4-M^) 

^ Z3(Li+L4+2iV/) + (M+i)(i?iL4+i?4Li-3/i?5)+i?5(L4-i¥)' ^3'^ 



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NoTi!^^^'] ^^^ AUDION OSCILLATOR. 225 

which, on collecting terms and calling Li + L4 + 2M = L© (the total 
inductance in the oscillation circuit), gives 

I ^ + y 

Z3L0 

This shows the ferquency to be determined largely by the inductance 
and capacity of the circuit. If all resistances Ru Ra, and Ri are zero, 
the equation reduces to 

<^-~. (33) 

These resistances, however, never are zero but are always of such a 
value as to affect the frequency somewhat. The fraction multiplying 
i/ZoC is always less than unity as no values can be given to i?4» -^si Lu 
and Lo which will produce a freely oscillatory circuit and make it greater 
than unity. The denominator contains 

I + -^ F (m + i), and ~ (m + i) and 

will always be equal to or greater than unity. This will always make the 
fraction less than unity. The adding of resistance to any part of the 
oscillator circuit will therefore increase the value of the denominator 
and reduce the computed value for the frequency. 

The effect of resistance in the circuit is therefore always to make 
the circuit oscillate at a frequency lower than the resonant frequency of 
the inductance and capacity. The greater the resistances, the greater 
this difference. The effect of the amplifying constant is to reduce the 
frequency still further. 

9. Oscillation "Damping** or '* Expanding" Term. 
Returning to equations 22 and 26 we can write the damping constant 

, ^ r (m+i)(L:L4"M^) ^1 

"^^ \2\Z^L,+ {n+l){R,L,+RJ.,-MR,)+R,{U-M)}\ 

Z3(i?l + i?4 + i?5) + (/X+l)(i?li?4- ^ + RaR^ 



»(34) 



where ofl is written for its equivalent value ZjX and L4 is written for 

This equation contains two terms multiplied together. In order that 
d\ may become zero or positive, one of these terms must be zero or 



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226 R. A, H EI SING. ^SSS? 

positive under certain conditions. The first term in brackets will always 
be positive. AP is always less than L1L4 as it is the mutual inductance 
between Li and Li and the positive terms in the denominator preponder- 
ate. The second term of the equation can be either positive or negative. 
If it is positive or zero, di will be positive or zero and our condition of 
free oscillations will occur. We can therefore say that in order to have 
the condition of free oscillations, that the circuit be constructed such that 

Zz{Ri+Ri+R,) + ifi+i) (riR4-^) +RJi,+ ^^^ 
0,2 ^^ ^^ ^:^- > o. (35) 

This equation can be put in a somewhat different form 

Z^{R^ + i?4 + Ri) + RkR^ + ^ + ^' 

M + I ^ -rz^ (36) 

i^\UU - il/2) - R,R, + - 

as the condition required in order that free oscillations will occur. The 
term co^ is left in this equation although an exact solution would require 
the substitution of its value from equation 32. However, the solution 
for (/x + i) is then very much more complicated. At the most, « varies 
from the resonant value for the circuit not more than a per cent, or so, 
and in practical work the error is of no consequence. 

Inspection of this equation shows that increasing any resistance in the 
circuit, tends to stop the oscillations. Also, that an audion with high 
output impedance Zz requires a higher value of /x in order to oscillate 
in a given circuit and that the high /x audion will oscillate where low m 
ones will not, other things being the same. 

If we put in the approximate value of co^ = i/LqC the equation becomes 

-^-^ R,R,C + M 

This shows that, other things being constant, increasing the capacity 
C not only lowers the frequency, but increases the value /* must have in 
order that the circuit will continue to oscillate. In a given circuit, with 
a given audion if C is increased, one of the resistances must be reduced, 
or vice versa. 

If we assume a circuit has no resistance whatever, a certain proportion- 
ment must still be made or free oscillations will not occur. If R\ = R^ 
= i?5 = o, the equation reduces to 



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JjJJ^j^'*] ^^^ AUDION OSCILLATOR. 227 

which gives 

This means that regardless of there being zero resistance in the oscilla- 
tion circuit elements, the amplification constant must bear the above 
relation to the circuit or it will not oscillate. If there is any ohmic 
resistance, the amplification constant must be greater. If the mutual 
inductance is zero 

f^ = x7i' ^"^^^ 

which shows that the ratio of the plate to grid inductances, and therefore 
the ratio of the reactive voltages on plate and grid must be equal to or 
less than fi. This relation can also be derived in a simpler way. In an 
oscillator circuit, the alternating voltage applied on the grid by the 
oscillation current will necessarily be 

Eg = coLi/o (41) 

and on the plate 

Ep = C0L4/0, (42) 

where /o is the oscillation current. The driving voltage of the fictitious 
generator in the tube is then 

Ea = MwLi/o (43) 

and it must be equal to or greater than the voltage drops in the plate 
circuit. 

M«Li/o = C0L4/0 + Zzh, (44) 

where h is the alternating space current. This gives the condition 

(45) 

as the required proportion which agrees with our earlier results, for, if 
the resistance of the oscillation circuit is zero, the impedance attached to 
the plate is infinite and h must ber zero. We have left then the same 
requirement for free oscillations as is given by equation 40 — 

>^« 

If the mutual inductance between L\ and.L4 is made zero, equation 
37 is further simplified. Experience has shown that the terms RJi^C 
and RiRiC are less than .1 per cent, of the other terms and we can further 
simplify by neglecting them. The equation then becomes 

, _ Z,(Ri + R4 + R,)C + L4 ^ ... 



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228 



R. A. HEISmO, 



[Sbcomd 
LSbbibs. 



where Lo = Li + L4. This is also equal to 

CL L 

L0i±0i L01 



(47) 



This shows that with all resistance in the circuit zero, the amplification 

constant must still be equal to or 
greater than LJLi and that as the 
resistance is increased, the required 
value is a straight line function of 
the total resistance. Curves are 
plotted in Fig. 4 for the required 
amplification constant as a func- 
tion of the total resistance. These 
curves are for various ratios of 
L4/L1 with Li + Li the same in all 
cases. It will be observed that the 
curves for Li/Li=3 and LifLi = ^ 
have the same slopes. This means 
that the amplifying constant re- 
quired increases with resistance at 
the same rate in the two cases al- 
For the condition of Li/Li = i the 
This is because Li X L4 is a 

















y 














<**■ 


'X 


«« 




/ 








^\ 


J> 


7^ 


- It* 


il 








,^. 


> 










^ 


Y 






Z-^: 


^^ 




y 


/ 






y^ 


<' 


\ r 




^ 


7*~" 




> 


J\ 




'C» 












^ 


/^ 














/ 


^ 


















^ — 3 


5—1 


r-a 


5—! 


1 J 


iT-l 


r-) 


r-i 


?— f 


s — 



Fig. 4. 

Required amplification constant as a function 

of resistance. Circuit constants in Fig. 5. 



though it begins at different values 
rate of increase required is a minimum, 
maximum under this condition. 

Equation 47 also shows that in a given case with the ratio between L4 
and Li kept constant, the ratio of Lq to L4 kept constant, and the product 
Lo X C kept constant, we can increase the total resistance in a circuit 
and not change the oscillatory conditions provided we increase L\/C 
and therefore Lq/C in the same ratio. If therefore in a given case, it is 
necessary to vary the resistance and it is desired to have the same degree 
of oscillation, this can be accomplished by changing Lo and C in such a 
manner that their ratio changes in the same proportion as the resistance, 
keeping, however, the product Lo X C and the quotient La/Li the same. 

In Fig. 5 are two curves showing the resistance required to stop 
oscillators having similar circuit and audion constants but different 
amplifying constants. If m = 10, it requires a much larger resistance 
in a given case than if /n = 2. The curves are plotted for required re- 
sistence as a function of that part of the total inductance that is in the 
plate circuit. This shows that with Li and L4 approximately the same 
in value, the circuit will oscillate with a greater resistance than with 
other adjustments. When the constants of an audion are known, the 



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Vol. XVI.! 
No. 3. J 



THE AUDION OSCILLATOR. 



229 



value of Li which can produce oscillations with a maximum resistance 
can be secured from the maximum value of equation 47. Solving equa- 
tion 47 for R 

nLoLi - Li^iix + i) 



Ri + R, + R,^ 



(48) 



Z^CLo 
where Lo — Li is substituted for Li. The curves in Fig. 5 are plotted 

















'l.<fm^ 




1 










%H 






Z'tasiuw 


/60 


1 






/ 


' — ■ 


< 






fyu 


1 




/ 








\ 




icu 
inn 


1 




/ 








\ 


s 






lUU 
on 


^' 


/ 












\ 






80 


1" 


f 












\ 






SO 
un 


7 
















\ 




5/1 


/ 






I. 

9 


c 








\ 




cU 


L 


^ 




**-«? 


r 


:^ 


' '. 


\ 


|_^ 



/6 
/¥ 

to 

8 

t 























/< 












































































/ 




















/ 


1 


\ 
















(/ 






\, 










j^" 


%• 

r**— 




\ 










0^ 


;«^ 


J 






r^ 






.1 




r— 1 


^ 


' — ' 



Fig. 5. 
Resistance required to stop oscillations. 



Fig. 6. 

Amplification constant required as a func- 
tion of L4/L0 for free oscillations. 



from the above equation with La plotted in percentage of L©. 
dntiating with respect to Li and equating to zero we get 

Li _ n 

Lo 2{ii + i) • 



On differ- 



(49) 



This equation enables us to get the best coupling for working into high 
resistance circuits where we wish to have the greatest reliability in oscilla- 
tion. 

This does not mean, however, that under these conditions the audion 
will deliver the maximum power. On the contrary, this is not the case 
as other things enter into that. It only means that oscillations will 
occur in a circuit of higher resistance with this relation occurring than 
with any other arrangement. 

Figure 6 contains curves indicating the values of 11 required for various 
ratios of LijLfi for three cases of Ru Ra* and R^ each equal to o, i and 10 
ohms in the three cases respectively. As indicated by the curves, a 
minimum value of /x is required in a given case if the value of Li is chosen 
properly. The value of Li at which the minimum n is required can be 



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230 



R. A. HEISISG. 



secured from equation 50, which is secured by differentiating 47 with 
respect to La 



u = z,(j?, + /?. + J^^)4V^+z;(^r+€T^c - ^ ] • 



(50) 



10. Form of Expanding Constant d\. 
In Fig. 7 a Hartley circuit is given with audion and circuit constants 
such as can occur in practice. The resistance of the condenser R% is 




L,»jZ5mh 


/r-X 


L^mJ2Smh 


z^*9eso 


kl',(nmh 


H^'/ •km 


C^OOtmf 


/^»0mi0k/. 


Fig. 7. 




Circuit and constants for Figs. 8 


9 and 


10. 





^ 


\^ 


















40 




^ 
X 
















f0 


< 




> 














^Z0H^ 










\ 


V 












' — i 




,%4J.Kii 



Fig. 8. 
Variation of "undamping" constant di with 



resistance. 



assumed as zero as it usually is small compared to other resistances, and 
the value of R4 is given as i ohm. Curves are given in Figs. 8, 9, and 10 
of dx, u^, and d^ as a function of R\, R\ and Ra enter into the equation 
under these conditions in exactly similar ways and the curves can be 
assumed as a function of R^ with Ri as one ohm just as well. 

Figure 8 gives d\ as.a function of Ri and shows it to be almost a straight- 
line function. In fact the variation is too small to see on a curve. If 
we neglect most of the resistance terms in equation 34 and write 



di = 



(m+i)(LiL4-3P) 
2Z,Lo 



^2 - 



Z,{R,+R,)+^ + ^- iix+l)^ 



(51) 



(M+i)(LiL4-ilP) 

we have an equation which is a straight line with J?i or R^ as the variable. 
The error in the above is about 4 per cent, in this case with Ri = 70 ohms 
and proportionally smaller if R\ is smaller. The curve as computed and 
plotted is from equation (34). The curve shows that 66.5 ohms for Ri 
is the critical resistance of the circuit. For values below 66.5 ohms, di 
is positive and free oscillations occur. For values above 66.5 ohms, di 
is negative and oscillations die out. The circuit is then said to be stable 
or not freely oscillatory. If i?i is of the order of zero or i ohm, the ex- 



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Vol. XVI-l 
No. 3. J 



THE AUDION OSCILLATOR. 



231 



panding constant d\ is 80,000. In such a case in one eighty- thousandth 
of a second, the oscillations will increase to e times their value and keep 
on increasing in the same manner. In one forty-thousandth of a second, 
they will increase to e? and in one ten-thousandth of a second to e* 
(= 3,000) times the starting value. This increasing does not continue 
indefinitely as the characteristic curve departs from a straight line. 
Increasing Ri reduces di until it changes sign at Rx = 66.5 ohms. It is 
possible to give Ri such a value, close to the critical value and above it, 
that the oscillations will be only slightly damped and the initial oscillation 
produced by closing the switch will persist for several seconds. The 







^~"~ 










■""" 




■^■" 


■^^ 


9*Mf»* 




1*11^ 


u^ 






















< 




















l»t^* 














































^ 


Mm 




















K 


^Ima 
















f0 £0 M W r» to 70 BO f« 




/« 44 #• •• 4* «• M «» f» 


Fig. 9. Fig. 10. 




\ 


^aria 


tion 


of ( 


^w 


ithr 


esist 


ano 


e. 




Variation of clamping constant d\ with resistance 



sensitivity of the circuit then to a little resistance such as can be intro- 
duced by bringing a coin or other piece of metal near to the circuit, is 
sharply marked. 

II. Form of the Frequency Term. 
The value of (^ is shown in Fig. 9. At i?i = o it is very close to i/LqC 
and would have that value if R^ equaled zero also. Increasing Rx lowers 
the frequency and at the critical value it is 1.6 per cent, lower. 

12. D.C. Damping Constant. 
Figure 10 shows the damping constant dj as a function of R\, The 
predominating resistance term in this equation (27) is Z3, and Rx and 
Rk affect it but slightly. Their influence, however, is to raise the value a 
few per cent. (2.5 per cent.) between i?i = o and the critical value. 
This constant is always negative when conditions are such as to produce 
oscillations and is of such a large value that it has ceased to influence the 
circuit long before the oscillations have changed appreciably. 

13. Range for Accurate Use. 
In securing equations 26 from equations 25 it was assumed that 2dx 
was small in comparsion to ^2, and that d^ was small compared to «*, 
and to w' + 2dxd^, The order of magnitude of these values for Rx — \ 



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232 R. A. HEISINC. gSS 

in the circuit in Fig. 7 are 



dj = - 19. X io«, 
di = + .1 X io«, 
w* = + 3.027 X 10".. 



(52) 



The first assumption that di was negligible in comparison to dj, produces 
an error in da of i in 190 for the most highly oscillatory condition and 
less than that for other conditions in the oscillatory range. The error 
produced by neglecting di^ in comparison with o)^ is i in 300 under the 
same conditions and less toward the critical condition. The error pro- 
duced by neglecting di^ in comparison with w* + 2didi is I in 490 under 
the same conditions. We thus see that our assumptions were justified 
and that the solutions secured are not only accurate at and around the 
critical point, but that the errors introduced when using the solutions 
over the rest of the oscillatory range covered by the parabolic equation 
are comparable with the errors of measurement of the circuit constants. 

14. Starting of Oscillations. 

The manner in which an oscillator starts may be described as follows: 
On throwing on the plate voltage, the space current builds up according 
to the form /p (i — e^*^) and a transient oscillation is started in the 
oscillation circuit. This transient, instead of dying out as in ordinary 
oscillatory circuits, builds up, on account of the circuit damping constant 
di being positive. 

In a damped oscillatory circuit, the oscillations, theoretically, never 
become zero. In a circuit of this kind capable of oscillating, it is the- 
oretically possible to start the plate current through the audion and have 
no oscillations, and attach the circuit afterward and make it take an 
infinitely long time for the oscillations to build up. As long as no tran- 
sient starts in the circuit, no oscillations will result. The condition is 
equivalent to that of balancing an object on a sharp point. Such an 
object will never fall until something starts it. Similarly the audion 
oscillator circuit will never oscillate until something starts it. Prac- 
tically this condition is as impossible to attain as is the mechanical 
analogue given because there are all kinds of electrical disturbances 
traveling in the ether which will start it off the same as external mechan- 
ical disturbances would start off the unstable mechanical analogue. 
The oscillations once started, no matter how small, will increase with 
time until the stage of full oscillation is reached. 

The manner in which the current builds up in an oscillator is shown 
in Figs. II and 12. 



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No!"3^^^] ^^^ AUDION OSCILLATOR. 233 

Figure 1 1 shows the space current building up with the first closing of 
the switch and the subsequent alternating current as the oscillations 
increase. At the place where the saturation point of the filament, and 
the bottom of the curve come into play due to the oscillations having 
built up, the logarithmic increase according to these equations ceases 
and the space alternating current begins to assume a constant value with 




Fig. 11. Fig. 12. 

Space current of starting oscillator. Oscillation current of starting oscillator. 

the peaks flattened. At the same time the oscillation current in Fig. 12^ 
also stops increasing logarithmically and approaches a constant value 
which is the steady state condition. 

15. Other Requirements Indicated. 
If we take equation 18, which gives the requirements for oscillation, 
and make the mutual reactance between plate and grid circuits zero 
(W = o) we have 

ZaCZi + Zi + Zb) + Z4(Z5 + (m + i)Zi) = o. (53) 

If all resistances are zero, the above equation divides into two parts, viz: 

Z4(Z5 + (m + i)Zi) = o, (54) 

in which all terms are purely imaginary (except /x) and the product 
therefore real, and 

Zz{Zi + Z4 + Z5) = o, (55) 

in which Z3 is a pure resistance, Zi, Z4 and Z5 are pure reactances. The 
product is therefore imaginary. For (53) to be zero, both 54 and 55 
must separately be equal to zero. Z4 and Za cannot have zero values in 
a freely oscillatory circuit and therefore the parenthietical terms must be 
zero. This means in 54 that either Z5 or Zi must be negative — that is a 
capacitive reactance — while the other is inductance. Comparing, or 
substituting 54 in 55 show that Z4 = fiZi and is of the same sign. That 
means, if a circuit is constructed with the three elements Zi, Z4, and Z5 
as shown in Fig. 13, that if Zi is an inductive reactance, Z4 must also be 
an inductive reactance while Z5 must be a capacitive reactance or, if Zi 



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234 



R, A, H EI SING. 



TSm 
LSb] 



ICOMD 

.Snuat. 



is a capacitive reactance, Z4 must also be a capacitive reactance and Z§ 
must be an inductive reactance. Phase relations are then such that 
sustained oscillations will occur. 

16. Equations for Colpitis* Circuit (Fig. 14). 

The same equations can be applied to Colpitts' circuit and similar 
solutions result. The circuit is similar in form to the Hartley circuit 























/TT\ 




2 


X. 


® 


■ZT"' 




Fig. 13. 
Schematic diagram of an oscillator. • 



Fig. 14. 
Colpitts oscillator circuit. 



but has inductances instead of capacities and vice-versa. This circuit, 
however, has no mutual between Zi and Z4. Rewriting equation 18 
with W equal to zero, 



Z,(Zi + Z4 + Z5) + (m + i)ZiZ4 + Z4Z5 = o. 
Putting in the values for Zi, Z4, and Z5 to fit Fig. 14, 



Zi = i?i + T^r, 
aCi 



(56) 



Zfi = i?6 + aLt , . 



(57) 



Tve have 



^*{Rr+R^+R^+^+^+au)H.+i)[^+^+RrR.+^] 



+RJi,+^+Rj:.tfl+^=o. (58) 

C4 aC4 



Multiplying through by a^ 



+- 



Collecting in descending powers of a, 



-^+^^]+a'(i?*/?.+§^)+a'i?^.+-§=o. (59) 



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Vol. XVI.1 
No. 3. J 



THE AUDIO fr OSCILLATOR. 



235 



a\R4+Zz)Li+anZ»iRi+R^+Ri)+RtRi+^+{^+i)RiRA 



+a 



which has the same general form as equation 21 

o' + o^x + ay + z = o, 



+ (m+ 1)^=0. (60) 



(61) 



where 



y = 



Z,{Ri + R, + R,) + R,R, + ^+ (m + i)RiRi 
w 

(R, + Z^)U 



(2?4 + Zt)U 



3 = 



('^+^^c;c; 



(62) 



{R, + Zz)U ' 

The solution of a in this equation is somewhat different from that of 
the Hartley circuit. Referring back to equations 24, 25, and 26, it will 
be remembered that we neglected di in comparison with d2, and di^ 
in comparison with w^. In this circuit, the values of di and dz are such 
that we cannot neglect di in comparison with dz but we can neglect di^ 
and 2did2 in comparison with ccl^. This gives us 



w2 = y^ 



^2 = ; , 



rfi = i(- ^■■^2) = H^-^j. 



(63) 



Inspection of dz shows that it will always be a negative quantity which 
is to be expected since it is concerned with the direct current transients 
in the circuit. If we write the approximate value of w^ (which holds 
when i?i = i?4 = i?5 = o) we have 

(m + I) 



"^^ (R, + Zz)(Ci + C,) 

If fjL is zero, this reduf es to 

T 



(64) 



(65) 



{R, + Z,)iCt + C4) • 
which is the decrement in a circuit containing a capacity of Ci + Ct 



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236 R, A, HEISING, ^^ 

and a resistance of Ri + Za. The resistance 224 is not in series with both 
capacities Ci and d but in the assumption of w* = i/isCo it was assumed 
that Ri was zero which accounts for the discrepancy. On making 
R4 — o throughout as it should be to make the assumption hold, the 
equation assumes the exact and correct form for these conditions. 

The effective capacity of Ci and d in series is called Co in the following 
equations and equals {CiCa)I{Ci + C4). 

The value of w^ from equations 62 and 63 is 



(^ + 1) 






This equation shows that the frequency is determined by the oscilla- 
tion circuit is, Ci and C4 in series and that if Ru Ra, and R^ are zero, the 
frequency is exactly the resonant frequency. Varying the resistances 
causes the frequency to vary around the resonant value. Raising 
resistance Ri raises the frequency. Raising resistance R^ will also raise 
the frequency but not' in the same proportion as Ri will. Increasing R^ 
may either raise or lower the frequency depending upon the other circuit 
constants. This circuit operates at a frequency above the resonant value. 
The usual circuit constants when operating on an antenna are such as 
will cause the frequency to raise as Ri is increased but drop if Ri is 
increased. 

The oscillation damping factor is 



...i 



C1C4 C4 



iR^+Z^)L,w' {R*+Zi)U J ^^'^ 

which can be either positive or negative. For free oscillations, the 
equation must give a positive value for di or 

^r^ S Z,(i?i + i?4 + R,) + RiRi + & + (m + l)RiRi. (68) 
CiC4ftr C4 

Rearranging, 

(m + I) ( ^~^, - RiRi ) ^ Z»{Ri + R, + R,y+ RJi, + 1-' (69) 

or 

p + Z,{Ri + R, + RO +'R4R, 
^ + 1^"^-^ J . (70) 



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Na*3?^^*] ^^^ AUDION OSCILLATOR. 237 

This equation shows that increasing the resistances raises the value of 
fi necessary for free oscillations. If we put in the approximate value of a>^ 

^ + Zz{Ri +R, + R,) + RJi, 

^ + 1^- f (71) 

- RiRi 



C1 + C4 

and it becomes evident that the increasing of the resistances can be com- 
pensated for by increasing the ratio of L5 to (Ci + d). That is, when 
Ru Ri, or i?5 are increased, Ci and C4 must be both decreased. Decreas- 
ing Ci alone will compensate to a certain extent but when it gets small 
compared to d it has little influence. Increasing is will help as 
Lh/(Ci + d) is the predominating denominator term while L^/d is 
of the order of magnitude of the remainder of the numerator. 
If the resistances in the circuit are all zero, we have the condition 

' mS^ (72) 

as the requirement for oscillation. This holds even though the circuit 
dissipates no energy. It corresponds with the requirement of a zero 
resistance Hartley circuit as given equation (40). 

This type of circuit operates at a frequency slightly above the resonant 
frequency. The reduction in frequency due to the term i + (Ra/Zz) is 
less than the increase due to the added term. 

If we neglect the small term in equation 71 we can say 

^' -I- Zz(Ri + R, + Rs) 

M + I ^ — r » (73) 



C1 + C4 



M ^ Z^{R^ + R, + R,) ^^ (g§;) + ^;, (74) 

and calling Co the effective capacity of Ci and C4 in series. 

M ^ Z^{R, + ie* + i?6) ^' + ^ . (75) 

which is exactly similar to equation 47 in form but has the reciprocal of 

a capacity wherever equation 47 has an inductance and vice versa. 

Curves 4, 5, and 6 for the Hartley circuit are therefore applicable to 

this equation for the Colpitts' circuit if we substitute i/Ci for Li, 1/C4 

for L4, I /Co for Lo and 1/C5 for L^. 

Research Department op 

The American Telephone and Telegraph Co. 
AND Western Electric Co., Inc., 
July. 1919. 



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238 C. W. HEAPS. [iS^ 



AMPLIFICATION OF ELECTRIC CURRENTS IN THE 
BUNSEN FLAME. 

By C. W. Heaps. 

Synopsis. 
Modulation of Electric Currents in a Bunsen Flame; the Use of a Third Electrode. 
— ^When an electric current is sent through a Bunsen flame, entering and leaving 
the flame by platinum terminals, it has been found by the author that amplification 
effects similar to those in vacuum tubes may be secured by the use of a third elec- 
trode or grid placed near the lime-coated cathode in the flame. The potential of 
this grid is varied with respect to the cathode and direct current characteristic 
curves are given showing the current as a function of the grid potential. These 
curves are similar in appearance to those obtained with the audion. and may be 
utilized in the customary way for calculating the amplification constants. The 
factors influencing these amplification constants are discussed and it is found that 
under what are probably the most favorable conditions of the apparatus used, 
the voltage amplification is but little greater than unity. The power amplification 
is about 108 and the current amplification about loi. The theory of the action 
is outlined in a general way. the effectiveness of the grid being ascribed to its re- 
tarding influence on the electron emission of the cathode. ^A consequent change in 
the cathode fall of potential alters the current through the flame. The utility of the 
device is not comparable with that of the vacuum tube amplifiers, largely because of 
the difficulty of securing permanent flame conditions. The energy output of the 
simple device used was also necessarily small because of the high flame resistance. 
It could be used, however, for the detection of electric waves. 

THE phenomena associated with the passage of an electric current 
through a Bunsen flame have been extensively studied by H. A. 
Wilson and others. It is found that if two clean platinum wires are 
used as electrodes in the flame, and if they are about equally heated, 
then the potential gradient in the flame between the electrodes is by no 
means uniform. In general there is a small fall of potential in passing 
from the positive electrode into the gas, a uniform and very small poten- 
tial gradient in the region midway between the electrodes, and a very 
large drop of potential in the immediate neighborhood of the negative 
electrode.^ Practically all the fall of potential in the flame is found near 
the negative terminal. This condition of affairs is to be expected in an 
ionized gas if the negative ions are much more mobile than the positive 
ions. The cathode fall of potential is caused by a deficiency of negative 
ions in the gas around the cathode, and the net result of this deficiency 

* H. A. Wilson: Electrical Properties of Flames and Incandescent Solids, p. 61. 



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Na*3?^^^*] AMPLIFICATION OF ELECTRIC CUR^RENTS. 239 

is that the greater part of the resistance to the passage of the current is 
located very near the cathode. 

Now when salt or lime is put on the hot cathode the drop of potential 
there is very much diminished and the potential gradient in the flame 
becomes much more uniform. Apparently the heated salt or lime by 
emitting electrons does away with the deficiency of negative ions in the 
gas near the cathode, with the result that there is a great decrease in the 
resistance of the flame to the passage of an electric current. The current 
through the flame may be increased as much as a hundred fold by this 
application of lime. It appears evident, therefore, that if one could 
regulate in a simple fashion the electron emission of the hot lime, then 
very large changes in the magnitude of the current through the flame 
could be effected. This regulation of electron emission from a hot wire 
is accomplished very effectively in the three electrode vacuum tubes of 
the audion type by a grid, or third electrode, the potential of which is 
adjusted by an outside battery. In this paper are described the results 
of using a third electrode for changing the magnitude of the electric 
current through a Bunsen flame. 

Preliminary experiments were made with the electrodes all in the form 
of straight wires placed parallel with each other and in a vertical plane. 
The top wire was made the cathode and sealing wax was burned on it. 
The residue of burned sealing wax contains calcium and barium oxides, 
is tightly adherent to the wire, and serves as an efficient source of elec- 
trons when heated. The straight wire serving as grid was placed below 
the cathode, having first been cleaned by boiling in hydrochloric acid. 
This grid was set very close to the cathode, its effectiveness being much 
greater when so placed. However, it was found that when the distance 
between grid and cathode was less than about half a millimeter particles 
from the sealing wax deposit collected on the grid when the wires were 
placed in the flame. As the grid functioned properly only when clean 
it could not, therefore, be placed too close to the cathode. The third 
wire, the anode, was a short distance below the grid. 

The anode and cathode were now connected in series with a galvan- 
ometer, a resistance, and a battery of dry cells. The grid was also 
connected through a battery and galvanometer to the cathode. The 
terminals were then placed in the vertical flame from a Meker burner. 
This burner was supplied with a mixture of gasoline vapor and air, the 
air being furnished by a compressor outside the room. A flame produced 
in this way is steadier and more homogeneous than when air from the 
room is taken in at the base of the burner by the usual method, because 
the entrance of dust and impurities into the flame is to some extent 



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240 



C. W, HEAPS. 



rsscoMD 
LSBxns. 



prevented. The whole arrangement of apparatus is shown in Fig. i. 
The galvanometer d had a resistance of 240 ohms and gave a deflection 
of one division for a current of two microamperes. The galvanometer G 
deflected one division for a current of 3.3 X lo""^ amperes and had a 
resistance of 235 ohms. The resistance R could be adjusted by steps of 
10* ohms from o to J2 megohms. .The component parts of the electrical 
system were insulated from the earth by ebonite blocks. 








Fig. 1. 



Fig. 2. 



Fig. 2 shows one of a set of curves obtained with this apparatus. The 
grid was 1.5 mm. below the cathode and the anode 3 mm. below the grid. 
The battery B had a constant electromotive force of 56.5 volts and the 
resistance R a constant value of 2 .megohms. The current flowing to the 
anode is plotted as ordinates in curve / and the current to the grid as 
ordinates in curve /'. Values of the grid current were multiplied by 10 
before being plotted and the grid current is considered as negative when 
it flows from grid to cathode through the galvanometer G. Similar 
curves obtained when -R = o show a greater effect of the grid potential 
on the main current to the anode than is indicated by Fig. 2. 

From inspection of the curves it appears that the applying of a negative 
potential to the grid has the effect of decreasing the main current and 
increasing the grid current. Such an effect can be secured only when the 
grid is free from lime, as in this case there is a large resistance to the 
passage of a current into the grid. Furthermore, with a clean grid the 
current produced in the grid circuit does not increase proportionally 
with the E.M.F. of battery ^, but at a slower rate if this E.M.F. is fairly 
large. This fact is a well known phenomenon in the case of flame 
conduction.^ However, as soon as the grid becomes sufficiently positive 
with respect to the cathode the grid current changes in direction and 
increases very rapidly with the grid potential. At this point the current 

^ Electrical Properties of Flames, p. 59. 



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Vol. XVI.! 
No. 3. J 



AMPUFICATION OF ELECTRIC CURRENTS, 



241 



flowing to the anode begins to diminish, — a result to be expected as a 
consequence of the deviation of current from the cathode through the 
grid into the flame; for when the grid is positive with respect to the 
cathode it functions as an anode, hence manifesting a comparatively 
small resistance to the passage of a current. 

It is apparent from the curve that a small change of current input 
caused a larger change in the current output, hence the device may be 
said to function as a current relay, or amplifier. If the effectiveness of the 
relay action is due to the retarding action of the grid potential on the 
electrons emitted from the cathode one would expect that another form 
might be given this third electrode so as to increase its effectiveness. 
The more completely the cathode is surrounded by the grid the greater 
should be the influence of the latter. However, the following points 
are to be considered. First, no part of the grid may be above the cathode, 
for in this position particles from the 
sealing wax deposit are carried upward 
and lodged on the grid, thus impairing 
its effectiveness as explained above. 
Second, the immediate proximity of a 
mass of metal exercises a cooling effect 
on the cathode, in which event the 
current flowing to it is considerably di- 
minished. In view of these facts the 
following arrangement was adopted. 
The tip of the cathode was bent up- 
ward, the bend being made about half 
a centimeter from the end, and the 
sealing wax deposit confined to the tip 
of this upturned wire. A spiral coil of 
platinum wire, containing three turns, 
about 0.7 cm. long and 0.65 cm. in di- 
ameter was placed concentrically around 
the upturned tip of the cathode. The anode was placed i cm. below 
this combination. The electric circuits outside the flame were set up a 
in Fig. I. 

Some characteristic curves obtained with this arrangement are shown 
in Fig. 3. Here, as before, the grid current, multiplied by 10 before being 
plotted, is given by curves /' and //'. The curves giving the current to 
the anode are correspondingly marked / and //. Each point on the 
curves // and /"/' represents the mean of two separate observations — the 
first set of readings being taken as the gird battery was being increased 



T 


I 


•" J 


-1 4Z 


tT^i^ 


^ 1^ u 


aSi- i t 


iso^ J y^"^^ 




J i e T 


/r^ T 1 


> r /J 


u \ \ 


^ Jlp if 


dMA^^I 2k 1 Sd/ 


TWr V|W/D «n iw J / *cm 



Fig. 3. 



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242 C. W. HEAPS. ^ISSf 

to its maximum E.M.F., the second set as it was being decreased. This 
method of observation was adopted in order to correct for slow steady 
changes which might occur in the nature of the flame or the lime deposit 
on the cathode. Such changes are difficult to prevent but in this case 
were found to be sufficiently small so that only one set of readings was 
taken for curves / and /'. For these curves the external resistance was 
that of the galvanometer, i,e,, 240 ohms; for // and //' a resistaitce of 2 
megohms was added. Curve / bends downward in a fashion similar to 
//when the E.M.F. of the grid battery is slightly greater than 60 volts. 
A comparison of Fig. 3 with Fig. 2 shows very clearly that the spiral 
type of grid is more effective in modifying the main current than the 
single straight wire. Indeed the general form of the curves of Fig. 3 is 
strikingly similar to the well known characteristic curves of vacuum 
tube amplifiers. An important difference, however, lies in the failure 
of the main current curves to approach so closely the axis of grid E.M.F. 
as is the case with the audion. It is impossible in a flame amplifier for 
the main current to be reduced below a certain minimum by altering 
the grid potential because the grid current is always an essential part 
of the main current, and furthermore, the grid current is always appre- 
ciable. 

In calculating the amplifying factors of this arrangement the same 
methods may be used as are practiced with vacuum tube amplifiers. 
The current is a function both of the E.M.F. of the grid battery and of 
the main battery B, so that the function expressing the relationship 
between these three variables will be the equation of a surface, called 
the characteristic surface. When a current flows between two clean 
electrodes in a flame it has been shown* by H. A. Wilson that the potential 
difference between the terminals is given hy E = al + bP where / is 
the current and a and b are constants. If the action of the grid battery, 
of E.M.F. F, is to introduce an E.M.F. in the main circuit, we might ex- 
pect the functional relation between the three variables to be of the type 

E + kV = al + bP, 

where E is the E.M.F. of battery B. Obviously this equation does not 
fit the curves of Fig, 3 over their entire length unless * is a variable. 
However, if we confine our operations to a region on the characteristic 
surface which is sensibly plane the equation may be written in the form 

E + kV^aL 

If E is kept constant and V varied we have k/d V = adi. The constant 
a may be considered as equal to i? + -Ro. where Rq is the resistance of 

» Electrical Properties of Flames, p. 62. 



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NaTaf^^*] AMPLIFICATION OF ELECTRIC CURRENTS. 243 

the flame between anode and cathode and R is the external resistance. 
The amplifying factor k is thus given by 

Jfe = (R + Ro)^ 

and its value may be obtained by reference to the curves of Fig. 3. 
The change, 61, in the main current is associated with a change H in 
the grid current — hence the current amplification may be defined as 
( = 61 /di. Obviously the change 6V in the grid battery will produce 
a change RSI in the potential drop across the external resistance. The 
ratio M = R8I/6V may be called the voltage amplification. The power 
developed in R by this potential change is RBP, The power supplied 
by the grid is 5V di. The power amplification is thus rj = RdP/BV8i. 
The above quantities may be expressed in the form: 

_dl _ kR _ Rik 



W '^ R + R^' ' R + Ro' 

In calculating the numerical values of these expressions it will be 
convenient to let 6 7 = 25 volts, the initial value of V being zero. Cor- 
responding values, then, of the other variables are for curves / and /': 
81 = 20.7 X 10"^, 5i = — 0.56 X IO"^ R = 240. For curves // and 
//' we have 81 = 13.4 X io~«, 8i = — 1.32 X io~^ and R - 2 X io«. 
The value of Ro is about 8 X lo' ohms for both curves. Substituting 
these numbers in the equations we get 





R = 240. 


^-axio*. 


k 


6.62 


5.36 


1 


370 


101.5 


M 


1.98 X 10-* 


1.07 


V 


7.32 X 10-« 


108.6 



There is thus no voltage or power amplification unless the external 
resistance is large. Even then the value of n is small as compared with 
ti for a vacuum tube amplifier. However, in a flame a large value 
is hot to be expected for the following reason. The action of the grid is 
supposed to consist in retarding or accelerating the electron emission of 
the cathode; hence, in order to be effective the grid must be instrumental 
in setting up an electric field of the proper value at the immediate surface 
of the cathode. Now throughout the range of the curves of Fig. 3 
where amplification is apparent a small current is flowing from the flame 
into the grid, and since the grid is free from lime there will be, therefore, 
a big fall of potential at the grid. A much larger current flows from the 



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244 ^- ^' HEAPS. [gSS 

flame into the cathode as a result of the much smaller potential gradient 
at this terminal. Suppose, now, that the grid is given a greater negative 
potential by increasing the E.M.F. of battery A by an amount 8 V. Since 
the fall of potential at the grid is caused by the driving of negative ions 
out of the region around the grid one effect of 8V would be to extend the 
region in which there is a scarcity of negative ions. For a sufficiently 
large 8V this region might be extended to include the cathode, with the 
result that the electron emission of the latter is retarded. The current 
to the cathode would thus be diminished. Evidence in favor of this 
view is found in the fact that the action of the grid is enfeebled by taking 
it farther away from the cathode. The potential change, SV, does not, 
therefore, produce a proportional potential gradient change at the 
cathode; we should expect this 67 to be distributed unevenly over a 
more extended region, a greater amount being located near the grid than 
at a distance from it. The net result of such a condition would be that 
6 F must be fairly large to produce much of an effect. A large 6 F means 
a small voltage amplification. However, the change, 6F, does not pro- 
duce a big change of grid current so the power supplied may be small, 
and power amplification is thus possible. 

In order to test out further the above theory of grid action some 
experiments were made with a lime-coated grid. Suppose that in some 
way the magnitude of the current taken in through the grid were a 
direct factor in diminishing the main current and that the potential 

drop at the grid were not an important 
factor. Then a lime-coated grid should 
function even more effectively than a 
clean one because in this case much 
smaller values of 5F are necessary to 
produce a given change in the grid cur- 
rent. However, experiments instituted 
to detect such an action failed to give 
any evidence in support of such a view. 
A given grid current change, 8i, in the case of a lime coated grid is asso- 
ciated with a very much smaller change of main current than is the case 
when the grid is clean. 

An ingenious method has been devised by Miller^ for determining k 
experimentally for the audion. His method as adapted for use with the 
flame is illustrated by Fig. 4. Here the resistances ri and rz are small 
compared with the flame resistance so that when the key K is closed 
E.M.F. *s are introduced into the grid circuit and the anode circuit which 
^ Proc. Inst. Radio Engineers, 6, p. 141. 1918. 




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NoTa^^^'] AMPLIFICATION OP ELECTRIC CURRENTS. 245 

are proportional, respectively, to fj and r 1. If these two resistances are 
adjusted so that the galvanometer G' is unaffected by the closing of K 
their ratio gives the value of k. Experimentally it was found convenient 
to make r2 = 100 and then vary fi. The values of k obtained were as 
follows: 





B.MJP. of B. 


Cturent Throuch G*. 


A. 


27.8 volts 
54.7 " 
95.0 " 


4.7 microamps. 
12.5 
16.5 


2.4 
4.0 
6.0 



The arrangement of electrodes and grid had been disturbed before 
these measurements were made so that these values of k cannot be 
expected to compare with those obtained from the curves of Fig. 3. 
Also, as the E.M.F. of battery B was increased the accuracy of measure- 
ment by the above method was considerably decreased. It is to be 
noted, however, that an increase of E.M.F. in the main circuit produces 
an increase of *, though some later experiments indicated clearly that 
there is little to be gained in amplification by having battery B greater 
than 150 volts. The internal resistance Ro is increased and the slope 
of the characteristic curve decreased when an E.M.F. of 580 volts is used 
in the main circuit. These results are probably produced by the setting 
up of larger potential gradients at the terminals. In a previous paper^ 
experiments are described showing that the gradient increases more 
rapidly at the anode than at the lime-coated cathode when the E.M.F. 
is increased, and that with the appearance of the large gradient at the 
anode the current does not increase so rapidly. The flame resistance 
would thus be increased ; and the fact that the gradient at the cathode 
increases explains why the grid would require a larger potential change 
to produce a given current change. 

It was found that when the flame was made hotter by the admission 
of more air the current through G' was increased. The value of k, 
however, was made smaller. Such an effect is to be expected if the theory 
of the action of the grid is as outlined above. For when the cathode is 
raised to a higher temperature we may expect more electrons to be 
emitted, thus diminishing still further the cathode fall of potential and 
hence increasing the current. But we also suppose the average velocity 
of the electrons emitted to be increased by the rise of temperature. 
Hence, to retard the emission by a given amount the grid requires a 
greater negative potential than was necessary before the increased 
heating. 

> Phys. Rbv., 7, 1916, p. 663. 



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246 C. W, HEAPS, 



L^RIBS 



The direct current characteristics of the flame amplifier may be deter- 
mined as above in a comparatively easy manner, but owing to the small- 
ness of the currents involved there is some difficulty in making quantita- 
tive measurements using alternating grid potentials. A sensitive 
telephone may be used as indicator but care is necessary if capacity 
effects are to be avoided. The question also arises regarding the presence 
of a time lag in the action of the grid. Such a lag is entirely inappreciable 
in vacuum tube amplifiers, but there is reason for searching for such an 
effect in a flame amplifier. When a battery, telephone, and flame are 
connected in series and the current made by closing a key the click in the 
telephone is less sharp and distinct than is the case if for the flame a 
pure resistance of equal magnitude is substituted. Apparently the cur- 
rent does not build up through a flame in the same fashion as through a 
pure resistance when the E.M.F. is applied. Indeed, one would not 
expect this to be the case, for a flame has been shown to behave like a 
capacity for high frequency electrical oscillations.^ 

These considerations seemed to make advisable a study of the time 
relations involved in the making and breaking of electric currents in a 
flame. A string galvanometer was accordingly inserted at G (Fig. i) 
and a number of photographs made using a photographic film mounted 
on a revolving drum, showing the motion of the galvanometer string 
as the grid potential was changed. Comparison photographs were also 
obtained when the galvanometer was inserted in a complete metallic, 
inductionless circuit containing a battery, and the current made by 
closing a key. These comparison photographs indicated that the time 
lag of the galvanometer string was 0.019 seconds. Inasmuch as there 
was no measurable difference between the comparison photographs and 
the photographs showing the change of flame current it is to be concluded 
that if there is any time lag in the building up or breaking off of a current 
through a flame this lag must be less than 0.019 seconds. 

The chief disadvantages at present apparent in the use of a flame 
amplifier for practical purposes are the smallness of the current output 
and the difficulty of securing steady and exactly reproducible conditions. 
In some instances, however, it may be used with convenience, e.g,^ in 
the detection of electric waves for class demonstrations, etc. The use 
of a third electrode, or grid, is of some interest theoretically and experi- 
mentally in that it affords a method of studying the mechanism of 
flame conduction. 

Thb Rice Institutb. 
Houston, Texas. 

» Electrical Properties of Flames, p. 100. 



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Second Series. October ^ iq20. Vol. XVI., No. 4 

THE 

PHYSICAL REVIEW. 



THE TONES FROM BELLS. 

By Arthitr Tabbr Jonbs. 

Synopsis. 

Normal Modes of Vibration, — The positions of the nodal lines are examined for 
partial tones up to the ninth. Certain partials are heard only when the bell is 
tapped on the sound bow. others only when it is tapped above the sound boW. 

Elasticity, — ^A value is obtained for the Young's modulus of bell metal. 

Striking Notes, — The principal striking note la the note which is best heard when 
tunes are plasred on bells* and which gives its name to a bell. It cannot be picked 
up from the bell by a resonator, it cannot be elicited from the bell by resonance, 
and it does not beat with a tuning fork of nearly its own pitch. No partial tone of 
the bell has the same pitch as this striking note, but the fifth partial is an octave 
above it. A striking note is not a difference tone, and it does not arise from com- 
pressional waves running through the material of the bell. The pitch of the striking 
note seems to be determined by the fifth partial, the octave in which it lies being, 
however, generally misjudged. A possible reason for this general failure in correct 
estimation of the octave is found in the rates at which the different partials reach their 
maximum intensities. 

A secondary striking note, an octave below the fourth partial of the bell, can be 
heard when the bell is tapped above the sound bow. 

I. Introduction. 

BELLS have been a subject of interest to many investigators/ but 
from the physical point of view very little work has been done. 
Papers by Lord Rayleigh/ Canon A. B. Simpson,' and Mr. P. J. Blessing* 
contain practically all that is known.* 

> For bibliography of more than 250 titles see H. B. Walters. Church Bells of England, 
London, Frowde, 19 12. 

« Phil. Mag., (5), 29, p. I, 1890, or Theory of Sound. $ 2350. 

» Simpson's two popularly written articles on "Why Bells Sound Out of Tune" and "How 
to Cure Them" were published in the Pall Mall Magazine, Oct., 1895, and Sept., 1896. 
They have also been published in the form of a booklet, which I believe is out of print. Lon- 
don. Skefi^gton, 1897. 

* Physikal. Zeitschr., 12. p. 597, 191 1. 

» From the last number of Science Abstracts (Jan., 1920) I learn of two publications on 
bells by J. Biehle. The copy of the Physikalische Zeitschrift in which these are reviewed 
(Vol. 20, pp. 429-431, Sept. 15, 1919) has not yet reached Smith College. I have, however, 
succeeded in seeing the review, and from it I judge that the material in my paper is sufficiently 
different from Biehle's to make it worth publishing. From the review of Biehle's work, from 
my study of the bells of the Dorothea Carlile chime, and from Simpson's statements about 
English and continental bells I think it likely that the bells of the Dorothea Carlile chime are 
more like English bells than like the 450 bells which Biehle has examined. 

247 



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248 ARTUUR TABER JONES, [fSSSS 

Rayleigh used a set of Helmholtz resonators and examined the partial 
tones given out by each of a number of bells. E^ch resonator was tuned 
by covering its mouth to a greater or less extent with a finger, and then 
the various partial tones of the bells were picked out by ear. In seven 
out of the eight church bells which Rayleigh examined the fifth partial 
was the only tone, irrespective of octave, which was close to the note 
that the bell was said to give, and in the case of at least one of the bells 
this fifth partial was an octave higher than the note which the founders 
gave as the pitch of the bell. 

Simpson's description of his method of study is given in a single 
sentence: **Any note of a bell can be elicited separately by touching the 
bell with the stem of a vibrating fork which is of the same pitch as the 
note in question." Simpson examined a considerable number of bells 
and came to regard as the most important partials three tones which 
are usually in the neighborhood of three successive octaves. The lowest 
of these three is the hum note, which is the lowest tone given by the bell. 
The next is the so-called fundamental, and for the highest of the three 
Simpson introduced the term nominal. Simpson adduced reasons for 
believing that when English tuners tuned a peal of bells they tuned the 
nominals and paid little attention to the other tones, whereas continental 
tuners paid most attention to the fundamentals. He also remarks, 
"There is further this curious fact: That while a tuner [English] always 
gave the nominal as the note of the bell, he invariably gave the pitch 
an octave lower than it really was." Simpson pointed out that for the 
finest musical quality all the partial tones of a bell should harmonize. 
This they seldom do. The interval from the hum note for instance to 
the fundamental he found was usually less than an octave, and the 
interval from the fundamental to the nominal somewhat over an octave. 
Simpson suggested a method of tuning bells which appears to depend on 
the fact that different partials have nodal circles at different distances 
up the bell. Thus by thinning the bell at certain distances from the 
bottom certain partials may be more affected than others. The results 
thus obtained are said to be very fine.* 

Blessing distinguished the principal note or striking note of a bell from 
its secondary notes. The striking note is the note which is usually most 
noticed when tunes are played on bells. The secondary notes are pro- 

1 Simpson's method of tuning was at once taken up and developed by John Taylor and Co. 
of Loughborough, Eng. As to the results see T. L. Papillon, Encycl. Brit., ed. 1 1, article Bell; 
Lord Grimthorpe, Clocks. Watches, and Bells, ed. 8. p. 393, London. Lockwood. 1903; W. W. 
Starmer, Carillons, p. 12, London. Novello, 191 5; W. W. Starmer. Musical Times, 60, p. 522, 
Oct. I, 1919. There are in North America three chimes by Messrs. Taylor — one of 10 bells 
at the Iowa State College, one of 13 bells at St. John's Church, Peterborough, Ontario, and 
one of 12 bells at the University of California — cast respectively In 1899, 1911, and 1915. 



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Na*4?^^^*] ^^^ TONES FROM BELLS. 249 

duced by division of the bell into segments separated by nodal lines, and 
are therefore the various partial tones of the bell. These partial tones 
can be picked out by properly tuned resonators and can be elicited from 
the bell by resonance. The striking note, on the contrary, sound no 
louder with a resonator than without it and cannot be elicited from the 
bell by resonance. The pitch of the striking note is usually not far from 
that of the second partial, but the manner in which the striking note is 
produced is a mystery. 

These remarkable statements as to the striking note of a bell, and the 
curious fact observed by Rayleigh and Simpson that the pitch of the bell 
appears to be an octave below the fifth partial of the bell certainly suggest 
some interesting problems. The installing of the Dorothea Carlile chime 
of twelve bells^ at Smith College provided opportunity for a study of 
the striking note and also for comparison of the partials of a number of 
bells, all cast in the same year and by the same founder. 

2. Method of Study. 

Pitch Determinations. — ^The partial tones were found by Rayleigh's 
method with the use of Helmholtz resonators. The striking notes were 
picked up without resonators. The pitches, both of partial tones and of 
striking notes, were obtained by ear by comparison with a sonometer 
which carried a wire one meter long. Two positions of the sonometer 
bridge were found such that a note from the sonometer was in one case 
just perceptibly sharper and in the other just perceptibly flatter than 
the tone in question, and the mean of these two settings of the bridge 
was used. In order to avoid errors due to large amplitude the sonometer 
wire was plucked gently and the tuning fork was tapped lightly. As 
standard a C4 [= 512 vd] tuning fork by Konig was used, and pie sono- 
meter wire was frequently compared with it. 

The accuracy of the pitch determinations seemed at the time of 
making an observation to be often as good as 5 cents,^ but observations 
made at different times usually differed by much more than this. The 
average deviation of half a dozen to a dozen observations made at different 
times was usually not far from 15 cents to 20 cents.' 

Calibration of Sonometer. — For the shorter lengths of the sonometer 
wire the frequency of the note from the wire was not accurately pro- 
portional to the reciprocal of the length. This appeared to be due 

» Cast in 1919 by the Meneely Bell Company. Troy, N. V. Total weight 11,838 lbs. 
[» 5370 kg.] Weights of largest and smallest bells respectively 3006 lbs. [•■ 1364 kg.] and 
268 lbs. [» 122 kg.]. 

* In designating intervals I use Mr. Ellis's very convenient interval the ceiU, 100 of which 
make an equally tempered half step. 

' I per cent, change in frequency corresponds to a change in pitch of 17.2 cents. 



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250 ARTHUR TABER JONES. ]^Sm, 

partly to the natural stiffness of the wire and partly to the increased 
tension when the bridge approached the end of the wire. In order to 
calibrate the sonometer two methods were used. For the range from Ct 
to Ci settings of the bridge were made at pitches which corresponded 
to a dozen selected notes on a reed organ which had a stop tuned to the 
untempered scale. Care was used to blow the organ at a pressure at 
which the tuning was good. For the range above c^ it was at first thought 
that the first, second, third, etc., overtones of any part of the wire might 
be taken as the octave, twelfth, double octave, etc., of the note given 
by that part of the wire, and therefore that corresponding to any chosen 
position A of the bridge the positions for the octave, twelfth, double 
octave, etc., would be those which gave the same notes as the corre- 
sponding overtones obtained with the bridge at A. This, however, 
assumed that the natural stiffness of the wire was negligible and did not 
prove satisfactory. The method was therefore modified. No attempt 
was made to get the overtones of the wire, but the octave was estimated 
by ear, and only the octave was used. Thus corresponding to any 
chosen position A of the bridge two other positions were found, one at 
which the pitch sounded a trifle flatter and one at which it sounded a 
trifle sharper than the octave of the note given at A. The mean of these 
two was taken as the setting for the octave of the note given at i4. In 
the range where this method overlapped the calibration from the reed 
organ the agreement of the two methods was very satisfactory. The 
corrections obtained have been applied to all readings, although for 
pitches below fi they are not more than 10 cents. In the neighborhood 
of Cs they amount to about 18 cents, and in the neighborhood of gs to 
nearly 25 cents. 

Temperature Correction. — ^The pitches if the bells appear to be very 
little affected by changes in temperature. Throughout the later part of 
the work the temperature was read at frequent intervals on a thermometer 
hung near the bells. The temperatures ranged from 10® C. to 30° C. 
The pitch of the hour bell — low/ of the chime — in the range from — 15° 
C. to 0° C, and the pitches of both the transverse and the longitudinal 
vibrations of a straight bar of bell metal in the range from — 10° C. to 
+ 20° C. were also determined. The temperature coefficients obtained 
in the different cases were small and were not consistent. 

It is not difficult to show that for the transverse and longitudinal 
vibrations of a straight bar, and for the extensional and flexural vibrations 
of a thin ring, 



» = no ( I H ^ / 1 , 



(I) 



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Nolr4.^^'] ^^^ TONES FROM BELLS, 25 I 

where n and »o stand for the frequencies when the bar is respectively at 
temperatures / and o*', and a and y stand for the temperature coefficients 
respectively of linear expansion and of Young's modulus. For many 
metals a + 7 is negative, and the pitches of such bars and rings therefore 
fall with rise of temperature. Since equation (i) holds for all four of 
these cases it seems],likely that it will also hold for bells. Talking a for 
bell metal as 0.000018 per degree C./ and 7 as — 0.0003 P^r degree C.,^ 
equation (i) leads to a temperature coefficient of about — 0.24 cent 
per degree C. 

In view of the lack of consistency in the experimental values for the 
temperature coefficient of pitch of the bells, and of the small value which 
such a correction would have, it was finally decided to make no attempt 
to reduce readings to a common temperature. 

Pitch as a Function of Amplitude. — ^Throughout most of the work it 
was thought that the pitches of many of the partial tones — especially of 
the lower partials of the larger bells — ^were somewhat lower when the 
bells were first struck than when the sound had nearly died out. This 
effect was not confirmed by the frequency with which properly tuned 
forks would beat with the tones in question, and was probably a case 
of the subjective lowering of pitch which has been discussed by Dr. C. V. 
Burton.' The pitches given below are averages from values which were 
obtained when tapping the bells gently. 

3. The Partial Tones of the Bells. 
Nodal Lines. — Rayleigh determined the number of nodal meridians 
for the first five partials of two bells. His method was to find a number 
of successive meridians at which the beats of the tone in question 
vanished. The number of nodal meridians is then half the total number 
of the meridians at which the beats vanish. In the case of the sixth 
partial of the largest bell of the Dorothea Carlile chime this method 
failed. Instead of two normal modes of vibration which gave a single 
set of beats for this partial there seemed to be several normal modes of 
nearly the same frequency, so that there were beats of several different 
frequencies. The frequencies of the most prominent beats varied in an 

> From the Landolt and BOmstein tables. This is about the value given for brass and for 
a bronze. 

• From values found by Kiewiet [Winkelmann, Hbduch. d. Phsrs.. ed. a, Vol. i, p. 567I 
for the temperature coefficients of various copper-tin allo3rs. Kiewiet *8 values have evidently 
been multiplied by some factor. On comparing his values with those for various substances 
at given in the Landolt and Bernstein tables I think it likely that this factor is io<, and have 
80 assumed. The coefficient given above is for the proportion of Cu 78 per cent, to Sn 22 
per cent, which is the proportion used by the Meneely Bell Company. 

» E. H. Barton, A Text-book on Sound, p. 579. 



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252 



ARTHUR TABER JONES. 



rSacoMD 
ISnass. 



erratic manner with the position at which the bell was tapped and the 
position at which the resonator was held, both along a circle of latitude 
and along a meridian. These variations may be partly due to the long 
inscription on this bell. 

After some time spent in trying to unravel these different beats 
another method of determining the number of nodal meridians was hit 
upon which proved entirely satisfactory and was in most cases much 
more expeditious. The resonator was connected to the observer's head 
by a piece of rubber tubing and the binaurals of a stethoscope. A single 
position was found where the beats vanished, the bell was tapped at this 
one position, and the resonator was moved quickly some distance around 
the bell. At the nodal meridians the sound grew faint and between them 
swelled out. This method proved to be also of service in cases where no 
beats could be detected and Rayleigh's method would have involved 
fastening to the, bell a local load. 

As regards nodal circles, Rayleigh observed that certain partials were 



Table I. 

Nodal Lines, 
In this table the positions of nodal circles are indicated by fractions. The unit chosen is 
the distance measured along the outer surface from the bottom of the bell to the point where 
the vertical ''shoulder" joins the more or less horizontal "crown." Numbers in parentheses 
give the average deviations of the measurements on the different bells. The middle of the 
"sound bow" is at 0.164 (0.007). 



PutkO. 



Bells on 

which 
Obs«r?ed. 



5«-«f I Positions o< 
Wo(tol nodal Circles. 
Mendiens. 



1 


All 


= hum note 




2 


All 


lundamentai 
3 


All 


4 


All 


5 


All 


= nominal 


,. 



None 

I 0.33 (0.015) 

0.47 (0.012) 
None found 



8 0.48 (0.017) 



6 

7 
8 
9 



I 6 largest 

I 6 largest 

2 largest 

1 largest 



8 
10 
10 
12 



0.20 (0.009) 
0.53 (0.033) 
None found 

None found 

None found 



Not certainly detected when bell 
was tapped below 0.21 (0.014). 

Very clear when bell is tapped on 
sound bow. Faint for other posi- 
tions of tapping. On five smallest 
bells not detected when tapping 
above sound bow. 

Detected only when tapping below 

0.37 (0.035). 
Detected only when tapping above 

0.46 (0.025). 
Detected only when tapping below 

0.37. 



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Vol. XVI.1 
No. 4. J 



THE TONES FROM BELLS. 



253 



very faint, if heard at all, when the bell was tapped at certain latitudes. 
My results check his very well and extend the observations beyond the 
first five partials. They are given in Table I. It will be seen that 
vibration of the material in the sound bow — on which the clapper 

Table II. 

Piickes of the Tones, 

In the upper half of this table pitches are given on the basis of ct » 256 vd. Calculations 
on the basis of as ■■ 435 vd. would indicate that all but onb of the bells are more or less flat. 
A note with no sign following it means that the value obtained did not differ from that equally 
tempered note by more than 10 cents; a note followed by + or — means that the value 
obtained did not differ from that note by more than 35 cents; and two notes mean that the 
value obtained lay between them, but did not lie as close to either as 35 cents. 

In the lower half of the table the pitches are in cents above the principal striking note. 
The three bottom lines give the average, the average deviation, and the range of values for 
the lower half of the table. 





Principal 

Striking 

Note. 


Pftrtial Tones. 


Bell. 


I. 


a. 


3. 


4. 


s. 


6. 


7. 


8. 


9- 


/ 
i 

ab 
a 

6b 
c 

db 
d 

«b 

/ 

e 


eb. 

/. 

it 

ob« 

0,+ 

6b.- 

Ct 

rfb4 

d,- 

«b.+ 

fi+ 

««- 


ob» 

atbbi 

bt- 

Ct 

/« 
gb, 

abi 
ai&bi 


«bi 

ebi 

gb,- 

gb, 

gi 

at 

C4 + 

bt-h 
db4+ 

«b4+ 

/4gb4 


gbagi 
flbi 
6b»6. 
bt 

rfb4+ 
cb4+ 

«4- 

U 

gb4 

ab4 

6b4+ 


CAd]^A 

dA+ 

eji 

figb* 

gi- 

g* 

a46b4 

6b4- 

rfbi- 
fb»- 


«b4+ 

f* 

g*+ 

ab4+ 

a4b]^4 

bb* 

C6 + 

d\?i 

£/.- 

«b.+ 

/5 + 

gbftgi 


04 

b]?4 

rfb.+ 

rfb» 

eb.- 

et- 


6b4 + 

C.+ 

rf.+ 

«b6^» 

«i+ 


«b6+ 
«b.+ 


eboet 


«b 

/ 

e 

ob 
a 

6b 
c 

rfb 
d 

eb 

/ 

e 




-969 
-891 
-936 
-939 
-922 
-909 
-956 
-930 
-875 
-915 
-904 
-926 


+ 2 
-203 
-118 
-206 
-220 

- 71 
+ 9 
-182 

- 65 
-224 
-188 
-131 


+349 
+298 
+341 
+292 
+289 
+358 
+310 
+26S 
+334 
+283 
+293 
+333 


+ 948 
+ 930 
+ 950 
+ 929 
+ 964 
+ 930 
+ 943 
+ 872 
+ 1000 
+ 955 
+ 961 
+ 922 


+1235 
+1200 
+ 1220 
+1224 
+1239 
+ 1239 
+1210 
+1197 
+1210 
+1202 
+1204 
+ 1172 


+1813 
+1693 
+1830 
+1692 
+1768 
+1808 


+1934 
+1923 
+1906 
+1946 
+1910 
+1933 


+2414 
+2213 


+2466 


Average 

Av. Dev 

Range 


-923 
20 
94 


-133 

71 

233 


+312 
26 
93 


+ 942 

21 

128 


+1213 
16 
67 


+1768 

50 

138 


+1925 
12 
40 


+2314 
100 
201 


+2466 



strikes — has little to do with the production of partials 4, 6, and 8, so 
that these partials are relatively faint when the bell is struck in the 



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254 



ARTHUR TABER JONES, 



rSvcoNs 

ISSRIBt. 



usual manner by a clapper, whereas in the production of partials 5, 7, 
and 9 the vibration of the material above the sound bow appears to be 
imimportant, and these partials — especially 5, which is the lowest of them 
— ^will be more strongly brought out by a blow of the clapper. 

The Pitches of the Patriot Tones, — ^The pitches of the partial tones are 
given in Table 11. It will be seen that it is only in a rather rough way 
that the successive partials form the same intervals for the different bells 
of the Dorothea Carlile chime. It will also be seen that in every case 
a partial of even order lies closer to the partial next above it than to the 
one next below, and an odd partial lies closer to the partial next below it 
than to the one next above. The averages for all bells are given in 
Table III. 

Table III. 

Average Interval Jrom One Partial to the Next. 



Partials 


1.2 


2.3 


3.4 


4.S 


S.6 


6.7 


7.8 


8,9 




Intervals in cents 


790 


445 


630 


271 


541 


158 


385 


52 







This difference in the intervals according as we pass up from an odd 
or an even partial may to some extent be understood by referring to 
Table I., where it is seen that the transition from an even partial to the 
next above it involves an increase in the number of nodal meridians, 
whereas the transition from an odd partial to the next above does not. 
For instance, on passing from the fourth partial to the fifth the width of 
each vibrating segment is reduced by about one fourth, whereas on 
passing from the fifth partial to the sixth the height of a vibrating seg- 
ment is reduced by something like a half. If nothing else changed we 
should therefore expect a larger interval between the fifth and sfacth 
partials than between the fourth and fifth. Table III. shows that this 
expectation is justified. 

4. The Striking Notes. 

Principal and Secondary Striking Notes. — From Table II. it will be 
seen that there is in general no partial which approximates at all closely 
to the pitch of the striking note. Thus Blessing's statement that a 
resonator does not respond to a striking note appears to be correct. 
Now when a bell is tapped on the waist or shoulder, i.e., above the sound 
bow, it is known^ that the bell sounds flatter than when tapped on the 
sound bow. And when tapping on the waist or shoulder I seemed to hear 
a note, flatter than the striking note, to which a resonator would not 

1 Helmholtz, Sensations of Tone. 4th Eng. ed., p. ^2. 



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N?Jr^*] ^^^ TONES FROM BELLS. 2$$ 

respond. I am therefore using the name principal striking note for the 
note obtained from the sound bow and not reinforced by a resonator, 
and the name secondary striking note for the note obtained from the 
waist or shoulder and not reinforced by a resonator. The secondary 
striking note is not as readily heard as the principal striking note. It is 
usually some 200 cents to 300 cents flatter than the principal striking 
note and somewhat flatter than the second partial of the bell. 

Resonance. — On two of the bells of the Dorothea Carlile chime the 
principal striking note is very close to the second partial. At some half 
dozen different times I thought that I picked up with a resonator the 
principal striking note of some one of the other bells, but later attempts 
with the same bells seem to show that I was mistaken. A resonator 
does not, in general, respond to a striking note. 

The results were similar when I attempted to get the bells to respond 
to a tuning fork which could be adjusted by moveable loads to give pitches 
throughout a range of about an octave. The bell was tapped and the 
fork adjusted by ear until its pitch was about that of the partial in 
question. The fork was then struck and its stem pressed against the bell. 
Various partial tones within the range of the fork responded clearly, 
but the striking notes did not thus respond. 

Beats. — ^There was no difficulty in tuning a fork until its pitch was about 
that of a given partial and then hearing distinct beats when both fork 
and bell were tapped. But no beats could be detected when the fork 
had approximately the pitch of a striking note. 

Difference Tones. — ^The first explanation of the striking notes which 
suggests itself is perhaps that they may be combination tones. Blessing 
says that Rudolph Konig suggested this possibility, but that no combina- 
tion of the partial tones of a bell would give the proper frequency. 
Blessing, however, gives no data in. support of his statement, and it 
seemed worth while to examine the question. 

If a striking note is a combination tone of any sort it is most likely 
that it is a first order difference tone. From the observed frequencies 
of the various partials the difference tones given in Table IV. have been 
calculated. This table has reference to the principal striking notes. A 
calculation for the secondary striking notes shows similar results. 

On comparing with Table II. it will be seen that Table IV. includes 
the difference tones arising from the fifth and seventh partials for all 
the bells on which the seventh partial was observed. But it will also be 
seen that in only half of these cases does the difference tone which arises 
from the fifth and seventh partials lie within a quarter of a step from the 
principal striking note. Moreover if the striking note were a combina- 



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256 



ARTHUR TABER JONES. 



fSECOND 

LSbriss. 



Table IV. 

Difference Tones. 
This table includes all the first order difference tones which lie within half a step from the 
principal striking note. Those which lie within quarter of a step are starred. 



Partialt. 


BeU. 


Cents from Prtn. Strik. Note 
Up to Dif . Tone. 


2.5 


Low eb 


+58 




c 


+13* 




d 


+85 




Highg 


+75 


4,6 


Low / 


-91 




a\^ 


-79 




a 


+59 


5,7 


Low e)^ 


+28* 




Low / 


+71 




Low g 


-22* 




ab 


+79 




a 


-55 




6b 


+15* 


7,8 


Low cb 


-40* 



tion tone we should expect it to be very faint, if heard at all, when the 
bell is tapped gently. As a matter of fact, the principal striking note 
comes out clearly when the bell is tapped gently. It seems then to be 
clear that a striking note is not a difference tone. 

Compressional Waves.— It seemed possible that the striking notes might 
be due to compressional waves which spread through the material of a 
bell and returned periodically to the point where the bell had been struck. 
If this were the case the frequency of the principal striking note would be 
roughly the same as that of the longitudinal vibration of a straight bar 
which had a length equal to half the circumference of the sound bow. 

To enable me to examine this matter the Meneely Bell Company 
kindly cast for me a rod of bell metal. After the ends had been trued 
off this rod had a length of 93.0 cm. The frequency of longitudinal 
vibration of the lowest mode was about 18 10 vd.* To have the same 
frequency as that of the low e\^ bell (304 vd) a rod of bell metal would 
therefore have to be 553 cm. long. The diameter of the mouth of the 

» The density of this rod is about 8.86 g./cc. Its Young's modulus is therefore about 
lO.O'io** d5mes/cm*. This value for the Young's modulus [bell metal » 78 percent. Cu and 
22 per cent. Sn] fits excellently on a curve codrdinating the values obtained by Voigt [Wied. 
An., 48. p. 674, 1893] for copper, tin, and an alloy of 88 per cent. Cu and 12 per cent. Sn* 
Voigt 's values were obtained by forcing a short bar of the given material to vibrate with a 
frequency of from one to two vibrations per second. 



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Na'4^^'] ^^^ TONES PROM BELLS. 257 

low eb bell is 134 cm., so that the rod required would havfe a length much 
greater than half the circumference of the sound bow — in fact consider- 
ably in excess of the entire circumference of the mouth. Similar state- 
ments hold for the other bells. 

Moreover, if the principal striking note were due to a compressional 
wave running, say, around through the sound bow, the diameters of the 
sound bows of the various bells should be inversely proportional to the 
frequencies of the principal striking notes. A calculation of the relative 
frequencies of the bells on this basis leads to values which are con- 
siderably in error — in the cases of three of the bells by something like 
100 cents. 

From this failure of the diameters of the bells to be proportional to 
the periods of the principal striking notes, and from the fact that a 
compressional wave would run through the material of a bell too quickly 
to give the observed pitch, it is clear that the principal striking note is 
not produced by a compressional wave. 

Misjudged Octave, — From Table II. it will be seen that the pitch of 
the principal striking note is not far from an octave below the fifth. partial 
of the bell. This checks with R^yleigh's and Simpson's observations 
that in most cases the only partial which is close to the pitch of a bell 
is the fifth, and that this fifth partial is an octave higher than the pitch 
of the bell is supposed to be. 

It is well known that an error of an octave in judging the pitch of a 
note is easily made, and Simpson evidently believed that there is in 
general no note which has the pitch of the principal striking note, but 
that we hear most clearly the fifth partial of the bell and think it is an 
octave lower than it is. If that is the case it would explain why a striking 
note cannot be picked up from a bell by a resonator nor elicited from the 
bell by resonance, and why it will not beat with a tuning fork. It would 
probably also explain a statement made by Blessing that if the sound 
bow of a bell is gradually turned thinner and thinner the striking note 
grows fainter and fainter and finally disappears. Blessing says nothing 
as to how this process affects the partial tones of the bell. But since the 
fifth partial appears to be produced almost entirely by vibration of 
material in the sound bow it seems likely that reducing the thickness of 
the sound bow would weaken the fifth partial. 

What evidence is there as to the octave in which the principal striking 
note lies? There is the judgment of the founders and tuners referred to 
by Rayleigh and Simpson. As to myself, I have at times felt very sure 
that the note I heard was really of the pitch which I have called that of 
the principal striking note and was not an octave higher. At other times 



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258 ARTHUR TABER JONES, liJS?£^ 

I did not feel so sure. .When the chime was being played I have com- 
pared the notes which I heard with those on a reed organ. When doing 
this it seemed to me there could be no question but that the pitches 
really are those which they are ordinarily supposed to be, i.e., each one 
an octave below the fifth partial. A statement from the Meneely Bell 
Company also corroborates this. With reference to the low / bell of 
the Dorothea Carlile chime they write me, **This is supposed to be about 
F natural above middle C, although bells as a rule, from their nature, 
seem to sound lower." The evidence seems to show that if the pitch 
of the principal striking note is determined by the fifth partial the 
octave is very generally misjudged — even by bell founders. 

Is there any probable reason for such an error in judgment? In 
attempting to answer this question we may exclude from consideration 
the fourth, sixth, and eighth partials, all of which are faint, if heard at 
all, when the bell is struck on the sound bow. From Table II. it will 
be seen that the seventh partial is almost exactly a musical fifth (700 
cents) above the fifth partial. Now in the harmonic series of tones to 
which the notes from strings, pipes, etc., approximate, we are accustomed 
to hear a fundamental accompanied by its octave and twelfth, so that 
even if the fifth and seventh partials do not produce a combination tone 
an octave below the fifth partial, they may nevertheless help to suggest 
a fundamental note of that pitch. 

Another, and probably much more important, reason for misjudging 
the octave lies in the rates at which the different partials reach their full 
intensities. The fifth partial seems to reach its maximum intensity 
almost as soon as the bell is struck, the second and third, especially on 
the larger bells, not quite so soon. Thus it is possible that when a bell is 
struck the fifth partial at once attracts attention, and the second and 
third add a considerable volume of sound so soon afterward as to make 
the pitch seem an octave lower than that of the fifth partial. On the 
smaller bells the second and third partials seem to be more prompt in 
their response, and this may have something to do with the difficulty 
which bell founders are said to have usually experienced in casting small 
chiu-ch bells of good musical quality. 

My present hypothesis as to the principal striking note of a bell is, 
then, that it is a note of which the pitch, except for octave, is determined 
by the fifth partial, and that the octave in which we think we hear it is 
determined by the more sluggishly responding second and third partials. 
It is desirable that a considerable number of bells should be investigated, 
and that photographic records should be obtained showing the rates 
at which the various partials, especially the second, third, and fifth. 



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Na 4'!^^*] ^^^ TONES FROM BELLS. 259 

grow to their maximum intensity when the bells are struck in the usual 
manner by a clapper. 

In conclusion I wish to express my thanks to the Meneely Bell Com- 
pany for their kindness in giving me various data and in casting for me 
the rod of bell metal. 

Smith College, 
March 30. 1920. 



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26o li. J. KELLY. fl;^?" 



ISbubs. 



THE VALENCY OF PHOTO-ELECTRONS AND THE PHOTO- 
ELECTRIC PROPERTIES OF SOME INSULATORS. 

By M. J. Kelly. 

Synopsis. 
Photo-emission from insulators; the valency of photo-electrons. — Charged droplets 
of different in^Iators are suspended in the field of a parallel plate condenser by 
regulating the strength and direction of the electric field so that the electric force 
on the droplet is equal and opposite the gravitational force. Ultra-violet light 
of various intensities and frequencies is allowed to fall on the droplets and the 
photo-emission is observed. The photo-emission of several insulators is studied 
in this manner. By making the light intensities sufficiently low, the author finds 
that only one electron escapes at each emission. This is true for all insulators studied 
and is verified in the case of each insulator by the observation of several hundred 
emissions. This result is in line with similar work on ionization of gases by X-rays. 
7-rays, /3-particles, and a-particles by Professor Millikan and his students. By . 
the use of different absorption screens the long wave-length limit of photo-emission 
from sulphur, shellac, oil and paraffine is located. These are located with greater 
accuracy than given by any other methods. The effect of water vapor and various 
surface impurities on photo-emission is discussed. 

I. Introduction. 

IN 191 1 Millikan and Fletcher^ furnished the first conclusive evidence 
that the mechanism of ionization by X-rays, gamma rays and ff 
particles consisted in the detachment from the neutral molecule of one 
single elementary charge. Millikan, Gottschalk and Kelly^ by using a 
similar method found the same to be true for ionization by a particles 
of several different gases and vapors. Mr. J. B. Dereux,' at Professor 
Millikan *s suggestion, using the same general method studied the photo- 
emissioi> from mercury drops. This work gave evidence which indicated 
that only one electron was expelled from the mercury atom in the process 
of photo-emission. 

It would indeed be interesting if high speed particles of atomic size, 
high speed electrons and electromagnetic radiations of as widely differing 
frequencies as that of gamma rays and ultra-violet light all showed the 
uniform property of liberating one and only one electron from the atom 
in its ionization. 

» Millikan and Fletcher, Phil. Mag. (6), 21, p. 753, 191 1. 
« Millikan, Gottschalk and Kelly, Phys. Rev. 
* J. B. Dereux, Phys. Rev., ii, p. 276, 1918. 



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Na'i^^^*] ^^^ VALENCY OF PHOTO-ELECTRONS. 26 1 

As mentioned above Mr. J. B. Dereux suspended single mercury 
drops, charged statically in the process of vaporization in the electric 
field of a parallel plate condenser and allowed ultra-violet light to fall 
directly on the drops. At the instant of a change in speed, indicating a 
change in the charge on the drop by its photo-emission, the light was 
shut off and its speed measured. It was possible to calculate from the 
change in speed the number of electrons liberated. The majority of the 
changes observed were those corresponding to emission of single electrons. 
Since a number of changes corresponded to emissions of more than one 
electron it was thought worth while to extend the investigation to other 
substances. 

If the changes observed which correspond to emission of more than 
one electron were due to simultaneous emissions from different atoms 
on the surface, the chance of this could be decreased by using less active 
surfaces and decreasing the intensity of the radiation. In choosing 
surfaces whose emission currents would be small the insulators would 
naturally suggest themselves. They were selected for the further reason 
that this is the only method of study of photo-emission which is capable 
of furnishing very direct and very reliable information with regard to 
the photo-electric properties of insulators. 

II. Historical Survey of Photo-electric Work on Insulators. 
In the study of photo-emissions of insulators the general method of 
procedure has been to place a thin sheet of the insulator over the surface 
of one of the plates of a condenser, to apply an accelerating field, allow 
the radiation to fall on the surface and measure the current. In good 
insulators the surface charges up positively as the photo-electrons escape, 
until the potential gradient at the surface is sufficiently high to neutralize 
the accelerating potential and prevent the escape of further electrons. 
This gives a fatigue effect which makes consistent results difficult to 
obtain. Sheets of good insulators will remain for a long time in this 
polarized state and fresh samples of the material must be used. Using 
this general method Goldmann and Kalandyk* investigated the photo- 
electric effect in sulphur. Photo-electric currents were obtained when a 
source of ultra-violet light was used and the polarization effect mentioned 
above was encountered and studied. They found that the photo currents 
completely disappeared when a plate of glass was interix)sed between the 
source and the sulphur, which would indicate the long wave limit some- 
where below X 3200. R. Reiger* investigated a number of insulating 

» Ann. d. Phys., XXXVI., p. 589. 1911. 

* R. Reiger, Ann. d. Physik., XVII., p. 935, 1905. 



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262 M. J. KELLY. [^^ 

materials, and found a number including, ebonite, mica, sealing wax and 
glass that showed small emission currents when exposed to the h'ght of 
an electric arc. W. Wilson* examined shellac and found no emission 
with ultra-violet light. 

III. Experimental. 

The apparatus as described by Millikan* was used in the present work, 
with such changes as were found necessary in the problem. The ap- 
paratus consisted essentially of a parallel plate condenser with plates 
horizontal, the plates were 22 cm. in diameter and were separated 1.586 
cm. An ebonite strip surrounded the condenser, with windows set in 
at proper intervals; one for the illumination of the drop, one for ob- 
servation and one of quartz for admission of the ultra-violet light. 
Several small holes were bored in the center of the upper plate for the 
admission of drops and an electromagnetically controlled shutter was 
provided to close these holes when the drops were under observation. 
The condenser plates were placed in an air tight iron tank about 30 cm. 
in diameter and 50 cm. high. This cylinder was placed in- a tank, about 
50 cm. in diameter leaving a space between the walls of tank and cylinder 
which was filled with oil to hold the temperature constant. Tubes at 
the level of the condenser provided with vacuum tight, transparent 
windows ran from the outer tank into the inner tank at the proper places 
for admission of light for illuminating the drop, for observation, and for 
admitting the ultra-violet light. The windows in the ebonite strip were 
directly in front of these tubes. 

The space between the condenser plates was illuminated by the light 
from a right-angled carbon arc. The light was focused on the drop by a 
cylindrical lens. A telescope having a high magnifying power was used 
for observing the drops. In the focal plane of the eye piece was a scale, 
the smallest division of which corresponded to 2 mm. Observations were 
made through a window 150 degrees from the one through which the 
light entered. A stop watch was used in timing. 

The potential of the plates was furnished by 3,500 small lead cells 
giving a potential of about 7,000 volts. By means of a special switch 
the condenser could be charged, short circuited, or reversed by changing 
the position of a handle. 

For changing the charge on the drops X-rays were used. The X-ray 
tube was placed just outside the apparatus near one of the windows. 
The source of radiation, usually a mercurj' vapor lamp was placed on a 
line of centers with the center of the condenser, and opposite a quartz 
window. 

» W. Wilson. Ann. d. Physik.. XXIII., p. 127, 1907. 
* R. A. Millikan, Phys. ReV., 32, p. 349, 191 1. 



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Vol. XVI. 
No. 4. 



] THE VALENCY OF PHOTO-ELECTRONS. 263 



The drops of the various insulators were formed by getting the insu- 
lator in the liquid state and discharging it through an atomizer placed 
in the upper part of the iron cylinder and manipulated by air pressure 
from without. After atomizing there was always a rain of drops through 
the holes of the upper plate and one of proper gravity speed was selected; 
the shutter over the holes closed and the drop balanced by regulating 
its charge with X-rays. An electromagnetically controlled shutter 
over the quartz window was then lifted and the radiation allowed to enter 
until a change in speed showed an emission to have occurred, the shutter 
was then closed and the speed determined. From this speed and its 
speed under gravity the number of unit charges on the drop could be 
obtained and the difference between the number before and after emission 
gives the number of electrons emitted. 

The number of charges on the droplet was determined from the relation 



»-<-^i;)f' 



where n = number of unit charges. 

C = a constant for a given drop. 

ti = number seconds it takes drop to traverse a certain distance 

d under gravity. 
h = number seconds it takes drop to traverse the same distance 

d under the field V. 
V = potential across plates. 
In determining the spectral range of photo-sensitiveness of the various 
insulators the method followed was to balance a drop in the field and 
allow radiations of a certain range to fall on it and observe whether or 
not emissions occurred. A large number of drops were used for each 
range so that there was no uncertainty in any case. 

IV. Sulphur. 

Drops of sulphur were obtained by heating chemically pure sulphur 
to a proper temperature in a specially made atomizer. The atomizer 
was placed in the large chamber about 20 cm. above the upper plate of 
the condenser and heated by a coil which kept the entire atomizer at a 
temperature of 150® C. At this temperature the sulphur is in the form 
of a pale yellow mobile liquid and atomizes quite readily. The tempera- 
ture regulation had to be close in order to obtain satisfactory performance 
for at about 160® C, the sulphur changes to a dark viscous liquid which 
is too viscous to permit being atomized. The sulphur drops were always 
charged statically and a satisfactory drop was easily obtained. 

1 Millikan and Fletcher, Phil. Mag. (6), 2i» 753, 191 1. 



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264 ^- J' KELLY. gS2! 

At the b^inning of the work no special precautions were taken with 
the gas content of the chamber; it consisted of the air of the room freed 
fairly well of water vapor. The sulphur drops evaporated very rapidly; 
in fact so fast that all calculation of the number of charges on the drop 
or the changes in charge were made impossible by the enormous change 
in the size of the drop. Table I. gives the gravity speeds, taken at 5- 
minute intervals, of a drop held under observation for 30 minutes. The 
charge on the drop was varied by X-ray ionization so that as it evaporated 
it remained just balanced in the field. At 5-minute intervals the electric 
field was removed and readings were taken of its speed under gravity. 

Table I. 

Sulphur Drop No. 8. 
Time to pass over 50 divisions: 

1. 8.2 seconds. 

2. 10.4 ** at the end of 5 minutes. 

3. 13.6 •• 10 

4. 17.7 •• 15 

5. 28.0 " 30 

While evaporating the drops drifted badly and were soon out of the 
illuminated space. It was necessary to get rid of the evaporation 
before observations could be made. After a number of unsuccessful 
attempts the trouble was eliminated by boiling sulphur in the sealed 
chamber until the walls were coated with flowers of sulphur, and moisture- 
free air then allowed to stand in the chamber for days before the observa- 
tions were taken. While the drops still evaporated, the rate was slow 
enough so that no uncertainty was introduced into the calculations. 
Table II. gives data on a drop observed for one hour in the same manner 
as the drop in Table I. 

The readings given in Table II. for each time interval are the average 
of a number taken at each of the intervals. I was considerably surprised 
to find a variation of as much as 10 per cent, in successive timings, one 







Table II. 






Drop No. 27. 


Time to 


pass over 50 divisions: 


1. 


7.6 seconds. 


2. 


7.6 


'• at end of 15 minutes. 


3. 


7.4 


30 


4. 


7.0 


60 



taken immediately after the other as from experience in timing drops 
in another investigation I had acquired sufficient skill to check readings 
to .1 seconds. Upon examining a number of the drops under a micro- 



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Na'i!^^] - ^^^ VALENCY OF PHOTO-ELECTRONS. 265 

scope they proved not to be perfect spheres, but spheres with minute 
crystal faces on the surface. The amount of this deformation varied 
considerably from drop to drop being apparently absent in some. This 
seemed to offer grounds for a satisfactory explanation of the variations, 
for a change in the orientation of the drop between two different ex- 
cursions would change the resistance offered to its fall. In selecting 
drops for observation several timings of their gravity speed were taken 
one immediately after the other and if the variations were large the drop 
was discarded and another obtained. 

In studying the valency of photo-electrons the following procedure 
was employed; after a drop with a proper gravity speed had been selected 
it was given a sufficient positive charge by X-ray ionization to just 
balance it i» the field with the voltage used. The shutter covering the 
quartz window was opened and the radiations from a quartz mercury 
lamp allowed to fall on the drop until an increase in speed indicated an 
emission. The shutter was immediately closed and the speed. deter- 
mined. The shutter was again opened and the process repeated. This 
was continued until 4 or 5 emissions had occurred, then the drop was 
brought back to its initial number of charges with X-rays and the process 
repeated. Some of the smaller drops were started with an excess of 3 or 
4 electrons and emissions allowed to occur until the drop had lost 3 or 4 
electrons beyond the neutral point. This was not possible with the 
larger drops due to the electric force with the small number of unit 
charges and with voltages available being insufficient to balance the 
force of gravity. Some drops were kept under observation foi* two hours. 
57 separate emissions were observed on one drop and over 500 emissions 
were observed under good experimental conditions and calculated. ' 

When the observations were first begun the drops captured about as 
many electrons as they emitted. This was at first attributed to residual 
radio-activity as this same apparatus had been used by Millikan, Gott- 
schalk and Kelly (loc. cit.) in studying ionization by a particles and had 
had radium open in the chamber. But on running a blank, that is 
observing the drop for an hour with the shutter closed, the drop was 
found to capture but two electrons; so it was concluded that the plates 
were emitdng. In order to prevent this the plates were covered with 
lamp black, but the photo-sensitiveness was increased several hundred- 
fold, in fact, as soon as the shutter was opened the drop would capture 
electrons in such rapid succession that the individual captures were 
indistinguishable. This emissivity was most probably due to the carbon 
in the lamp black as it was found that its long wave limit was X 2550 
(approx.) and this is about the limit Hughes^ found for carbon. 

Hughes, Photo-Electricity, p. 102. 



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266 



M. J. KELLY. 



[Second 
LSbribs. 



Shellac was then tried, as W. Wilson (loc. cit.) had pronounced it not 
photo-sensitive to the light of a quartz mercury-vapor lamp. How- 
ever, it emitted electrons freely, so a thin coating of paraffine was next 
tried and no emission was found. 

Table III. gives the results of observation on lo droplets of sulphur. 

Table III. 



Drop No. 


No. Minutes Under Obs. 


No. BmiMiont. 


No. Sin^t. 


No. Molt 


21 


90 


35 


35 




22 


100 


40 


40 




24 


100 


44 


44 




25 


120 


57 


56 


1 


26 


30 


12 


12 




28 


60 


38 


37 


1 


29 


110 


45 


45 




30 


120 


40 


40 




31 


60 


20 


20 




32 


100 


25 


25 





As is shown all emissions with the exception of two were of a single 
electron and both of these were emissions of two electrons. As is evident 
from the ** times under observation " the emissions were very frequent, 
in fact more so than the table indicates as this time includes time con- 
sumed in regulating charge on the drop, timing it and adjusting the 
illumination. 

In order to decrease the rate of emissions a plate of fused quartz about 
5 mm. thick was placed in the path of the beam. From evidence to be 
discussed later this plate appeared to cut off all radiation below X2250. 
This decreased the emission rate to six to eight an hour. About 200 
emissions were observed at this reduced rate and 40 hours were consumed 
in observation. In every instance the emissions were unmistakably 
emissions of single electrons. Table IV. gives the data on a repre- 
sentative drop. 

The activity of various drops differed considerably. The rate of 
emission from some drops was so slow that after observing them for a 
time to be sure they possessed activity they were discarded. This 
difference in activity must be attributed to surface conditions. All drops 
were most active initially and their activity gradually decreased with 
time; the rate of emission was decreased roughly one half at the end of 
two hours. 

The surface polarization effect which was observed in sheets of sulphur 
was somewhat evident with the drops. If electrons were emitted until 
the drop became positively charged then as the positive charge increased 



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Vol. XVI.T 
No. 4. J 



THE VALENCY OP PHOTO-ELECTRONS. 



267 



Table IV. 

Drop No. 32. 



tl. 


h. 


K.Y. 


(-^)^.- 


Ho. Units on 
Drop. 


No. Blectront 
Emitted. 


4.1 


80.0 


24 


.0438 


4P08. 






12.6 


24 


.0552 


5 






7.0 


24 


.0660 


. 6 






4.9 


24 


.0765 


7 




4.1 


19.5* 


36 


.0219 


2Pos. 






22.4 


36 


.0330 


3 






7.1 


36 


.0436 


4 






12.2 


24 


.0557 


5 






6.8 


24 


.0672 


6 






5.0 


24 


.0756 


7 




4.0 


5.0 


24 


.0750 


7Neg. 






6.9 


24 


.0658 


6 






12.8 


24 


.0550 


5 






80.8 


24 


.0436 


4 






19.0* 


24 


.0328 


3 




4.0 


21.6 


36 


.0326 


3P08. 






7.0 


36 


.0434 


4 






12.0 


24 


.0552 


5 






6.8 


24 


.0660 


6 






4.8 


24 


.0763 


7 




3.9 


6.7 


24 


.0659 


6Neg. 






12.0 


24 


.0551 


5 






78.0 


24 


.0435 


4 






19.8* 


24 


.0334 


3 




3.S 


20.0* 


36 


.0221 


2Pos. 






22.0 


36 


.0325 


3 






6.9 


36 


.0430 


4 






12.0 


24 


.0547 


5 






6.6 


24 


.0656 


6 






4.9 


24 


.0738 


7 





All U marked with * the drop was going downward due to the force of gravity being greater 
than the opposite directed force of the electric field. In these cases the minus sign is used 



in the formula 



(■4:)- 



by further emissions, the rate of emission was greatly decreased. A drop 
that had lost 25 electrons beyond its neutral value was held under 
observation for one hour and only three emissions observed. The excess 
positive charge was neutralized by X-ray ionization and the drop was 
found to emit at the rate that was to be expected after it had been under 



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268 M. /. KELLY. [||^ 

observation for one hour. Data was taken on a number of drops with 
varying excess of positive charge hoping to find some quantitative relation 
of stopping potentials but the variation from drop to drop, probably due 
to differences in surface contamination masked any such relation, if it 
exists. 

In order to find the long-wave limit of emission for the sulphur a 
Hilger quartz spectroscope was set up outside the quartz window and 
by means of extra quartz lenses the radiation from any desired frequency 
was focused at the center of the condenser in the path of the drops. 
No emissions were obtainable with any frequency. To test the adjust- 
ment of the light system mercury drops were suspended between the 
plates of the condenser and photo-emissions were obtained when the 
instrument was set for X 2536. As no emission could be obtained from 
the mercury for the adjustments of the spectroscope at wave-lengths 
shorter than X 2536 due to their low intensity, the only conclusion that 
could be drawn from this work was that the long-wave limit for the 
sulphur was some wave-length shorter than X2536. It was next at- 
tempted to set some closer limits for the long- wave limit by using ab- 
sorption screens. 

After studying a number of filters Cobalt chloride in absolute methyl 
alcohol was found most suitable* An absorption cell with quartz windows 
about 8 mm. wide was used. Solutions of Cobalt chloride in this cell, 
varying in strength from 2 iV to .01 N were studied photographically 
with a quartz spectrograph and a mercury vapor lamp. The greatest 
precautions to prevent stray light and fogging were taken and the 
exposure times were made as long as fogging permitted. These photo- 
graphs showed the solutions to have a narrow absorption band covering 
the range X 4600 to X5100 and complete absorption of radiations of 
wave-lengths shorter than X 2650 for the 2 N solution, and of all radia- 
tions shorter than X 2400 for the .01 N solution. The methyl alcohol 
cut off all radiations of wave-length shorter than X2350. With the 
quartz mercury lamp that was used, photographing directly and using 
every precaution lines were obtained down to X2150. These photo- 
graphs were repeatedly taken and the sharpness and completeness of the 
absorption ranges well substantiated. 

No emissions from the sulphur were obtained when the radiations 
passed through the cell filled with any of the cobalt chloride solutions 
or with the methyl alcohol only. Many drops were held under observa- 
tion for more than an hour each with the methyl alcohol cell before the 
quartz window. After a drop was secured it was exposed to the direct 
radiations and several emissions observed then the cell would be inter- 



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VoL.^VI.J j>^^ VALENCY OF PHOTO-ELECTRONS. 269 

posed and tha emissions would immediately stop; at the end of 30 
minutes the cell would be removed and emissions from the drop would 
begin immediately in every instance. This definitely placed the long- 
wave limit at some wave-length shorter than X 2350. 

An absorption screen was looked for that would transmit some fre- 
quencies to which the sulphur was photo-sensitive; some transparent 
commercial fused quartz was found which when interposed in the path 
of the radiation cut down the emissivity from 40 emissions to the hour 
to 5 an hour. These plates were about 5 mm. thick and only one was 
used. If a plate of crystal quartz of the same thickness was placed in 
the path of the radiation there was no reduction in the rate of emission. 
This was verified in a number of drops. On examining the transmission 
of this plate it was found to cut off (at least photographically) all wave- 
lengths shorter than X 2250. 

Some time after completing this work I noticed that Hughes in his 
book, Photo-Electricity, had remarked that a column of water i cm. 
long cut off all radiations shorter than X2200. This was confirmed 
photographically and as a check on the earlier work, the emission of 
sulphur through this filter was examined and its rate of emission was 
found to be decreased in about the same ratio as with the fused quartz 
plate filter. 

The long-wave limit of photo-sensitiveness of sulphur can be placed 
with a great amount of certainty between X 2400 and X 2200 and it is 
probably within the narrower limits of X 2350 and X 2250. 

V. Shellac. 

Drops of shellac were obtained by atomizing a filtered solution of 
shellac flakes dissolved in ethyl alcohol. The alcohol evaporates rapidly 
and the density of the sphere reaches a constant value in a very few 
minutes, as is shown by the constancy of the gravity speeds. The drops 
showed perfect sphericity when examined under a microscope and showed 
none of the variations in speed on succeeding excursions under gravity 
as did sulphur. 

All the sulphur was washed out of the large cylinder and removed 
from the condenser plates. The entire interior of the iron cylinder was 
coated with shellac and this allowed to stand several days after which 
the air was pumped out of the tank several times and the air that was 
admitted each time was filtered and dried. A thin coating of paraffine 
was used on the plates as with the sulphur. The shellac drops were 
much more satisfactory to work with as there was no evaporation, and 
little, if any, fatigue effect of photo-emission. 



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270 



M. J. KELLY. 



rSBCOND 

LSbubs. 



P.D. ■■ 6,000 volU. 

Time under obe. ■■ 90 minutes. 



Table V. 

Drop No. 49. 



ii. 


ti. 


(-E)fx'^- 


No Units on 
Drop. 


NoJKlectrons 
Emitted. 


TimoLiterTml 

Before Bmis- 

■ion. Sees. 


23.0 


31.8* 


.0465 


IP08. 








51.3* 


.0920 


2 




20 ' 




128. 


.1367 


3 




90 




Inf. 


.1666 


4 




10 




62.0 


.2286 


5 




120 




35.6 


.2745 


6 




40 




25.0 


.3200 


7 









18.2 


.3775 


8 




80 




15.6 


.4125 


9 




30 


23.2 


35.4 


.2757 


6Neg. 








61.0 


.2296 


5 




15 




Inf. 


.1666 


4 




40 




130.0* 


.1370 


3 




65 




52.0* 


.0926 


2 




5 




32.2* 


.0466 


1 




10 




23.0* 


.0000 







12 




31.8* 


.0448 


IPos. 




28 


23.2 


Inf. 


.1666 


4Neg. 








133.0* 


.1375 


3 




68 




50.0* 


.0895 


2 




70 




32.0* 


.0462 


1 




10 




23.0* 


.0000 







25 


23.4 


32.2* 


.0461 


IP08. 








52.0* 


.0916 


2 




70 




134.0* 


.1375 


3 




45 




Inf. 


.1666 


4 




150 




62.5 


.2290 


5 




10 




35.6 


.2761 


6 




35 




25.4 


.3200 


7 




40 


23.4 


32.5* 


.0466 


1 Pes. 








52.4* 


.0923 


2 




140 




133.0* 


.1373 


3 




30 




Inf. 


.1666 


4 




25 




62.0 


.2295 


5 




100 




35.4 


.2766 


6 




75 




25.2 


.3211 


7 




5 




18.2 


.3808 


8 




2 


All h marked with * the drop was going downward due to the force of gravity being greater 


than the oppoi 


sitely directed 


force of the electn 


c field. In these 


cases the mini 


IS sign is used 



in the formula 



(-Ii) 



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Vol. XVI. 
No. 4. 



] 



THE VALENCY OP PHOTO-ELECTRONS. 



271 



With the complete radiation from the mercury vapor lamp the photo- 
current from the shellac drops was less than that obtained initially from 
the best sulphur drops. However there was much less variation in 
photo-emission from drop to drop than from the sulphur. 

The time interval from the opening of the shutter until an emission 
had occurred was observed for about 200 emissions. This was taken 
when the excess positive or negative charge was never more than 5 units. 
The average time interval was 50 seconds, the maximum time was 4 
minutes and the minimum was too small to be measured by a stop watch. 

In the study of the valency of the emission data were taken on 40 drops. 
More than 800 emissions were observed and the number of electrons 
liberated at each emission determined. The same procedure was fol- 
lowed as in the case of the sulphur. 

Table No. V. gives the data on a typical drop. The time interval 
given under ** time of exposure " is the interval of time between the 
opening of the shutter and the occurence of the emission. 

Table No. VI. contains a summary of data on 10 drops. 

Table VI. 



Drop. Ho. 


Time Under Obs. 


Ho. BmiMiona. 


No. Sinflet. 


No. Muh. 


17 


120 


47 


47 





19 


80 


29 


29 




20 


100 


28 


28 




21 


60 


23 


23 




27 


120 


44 


44 




31 


120 


40 


40 




37 


60 


19 


19 




3S 


50 


17 


17 




40 


70 


26 


26 




49 


90 


30 


30 





As seen from the table every emission observed corresponded to the 
liberation of a single electron, this was also true of the observations on 
the remaining drops. The conclusion thus seems fully warranted that 
the process of photo-emission liberates one and only one electron from 
the molecule in sulphur and shellac. This is rather interesting especially 
in the case of shellac in which there are complex molecules made up of a 
large number of atoms. 

As it is generally recognized that there is an absence of free electrons 
in non-conductors and insulators, the actual observation and identifica- 
tion of electrons emitted photOrdectrically from them gives added weight 
to the accumulating evidence that photo-electrons come from the atom 
structure and are not free electrons. 



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272 if. /. KELLY. ' [g^ 

The long-wave limit of the shellac was found to be quite definitely 
somewhat shorter than that of sulphur, although I believe not a great 
deal shorter. No emissions were obtained from a large number of drops 
when the radiations were passed through the methyl alcohol solution. 
A fused quartz plate was then interposed in the path of the beam and 
lo drops were observed for intervals of time exceeding an hour and no 
emissions occurred, but immediately after the plate was removed emis- 
sions would begin quite normally. The filter of water one cm. in thick- 
ness was interposed in the path of the beam for each of the lo drops and 
emission was entirely stopped, but immediately after removing the filter 
emission began in every case. The conclusion then seems fully warranted 
that the long-wave limit for shellac is shorter than X 2200. 

Allen in his book Photo-electricity, p. 83, in discussing W. Wilson's 
work says, ** Although shellac itself is not photo-electrically active, 
it allows the photo-electric current to pass through it when a thin layer 
is laid upon a metal plate." As is evident from what has been given 
we found that shellac was photo-sensitive. The photo-sensitiveness of 
shellac in thin sheets was examined by covering the metal plates of the 
condenser with a thin coating. The photo-emission from the coated 
plates was stopped by the same filters that stopped the emission from 
the shellac spheres; although this was not found to be the case with the 
cleaned metal plates, which indicates that this emission is from the 
shellac and not from the plates. 

VI. Paraffine and Oil. 

Commercial paraffine was melted and a thin coating of it placed on 
the condenser plates in a portion of the work with shellac and sulphur 
because there was no emission from it when illuminated by the mercury 
vapor radiation direct. 

The oil used throughout the work on the evaluation of ** e " by Pro- 
fessor Millikan was examined for its photo-emission by suspending the 
drops in the path of the radiation and found not to be photo-sensitive to 
the radiations from the mercury light direct. 

As only a small piece of fluorite just large enough for a window in the 
ebonite strip was available, a pair of zinc electrodes were placed just 
inside the inner cylinder and in the narrow space between the edge of 
the condenser plates and the wall, directly in front of the small fluorite 
window. By using a tuned circuit very much energy was put into the 
spark. When the spark was running it caused currents of air in the 
cylinder which made the drops drift badly. 

Great precautions were taken in sealing the condenser so that its 



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Na'^^^J ^^^ VALENCY OF PHOTO-ELECTRONS, 273 

interior would not be affected by outer currents. By doing this, drops 
of either oil or paraffine could be kept under observation for more than 
30 minutes while the spark was running. The drops of paraffine were 
obtained by melting the paraffine in the atomizer used for the sulphur. 
The oil drops were obtained by atomizing in the usual method. 

With the radiation from the zinc spark passing through a thin fluorite 
window and about 12 cm. of air photo-emissions were obtained from 
both the oil and the paraffine drops. Several emissions were obtained 
from each of 20 drops of both materials and no emissions were obtained 
from any drops of either material when radiations from the mercury 
lamp fell on the drops. The conclusion that both oil and paraffine are 
photo-sensitive and that their long-wave limit is shorter than X2150 
(this is the shortest wave-length photographed through the mercury 
lamp used) seems fully warranted. 

VII. Summary. 

1. A method has been given for detecting very weak photo-emission 
currents from insulators. Photo-emission currents were observed from 
sulphur, shellac, oil and paraffine. 

2. The long-wave limit for sulphur has been placed between X 2400 
and X 2200. 

3. The long-wave limit for shellac was found to be some wave-length 
shorter than X 2200. 

4. The long-wave limits for oil and paraffine were found to be below 
X2150. 

5. The photo-emission from molecules of sulphur and shellac consist 
in the ejection of a single electron from the molecule at each emission. 

This work was suggested by Professor Millikan and carried out under 
his direction. I desire to express my appreciation for his interest and 
helpful suggestions, also to Mr. V. H. Gottschalk who was associated 
with me in the preliminary work. 



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a 74 ^- O. HULBURT AND G. BREIT. (aSS? 



THE DETECTING EFFICIENCY OF THE ELECTRON TUBE 

AMPLIFIER. 

By E. O. Hulburt and G. Brbit. 

Synopsis. 
Definition of DeUc^ing Efficiency. — The detecting efficiency of an amplifier is 
defined as lim --r where &• is the average change in the plate current of the last 

tube and A is the amplitude of the impressed grid voltage. 

Relative Importance of Detecting Efficiency and Input Impedance, — ^A discussion 
of the necessity of taking into account both the detecting efficiency and the input 
impedance is given. 

Measurements of Detecting Efficiency for a Transformer-Coupled Radio-Frequency 
Amplifier, — Measurements of the detecting efficiency of a tiansformer-coupled radio- 
frequency amplifier were made by means of a condenser potential divider and a 
sensitive quadremt electrometer. 

Measurements of Amplification. — Measurements of the amplification due to 
each tube of the above amplifier were made. It was found that the sound intensity 
in the telephones was increased in the ratio of 9 X lo* : i owing to the use of the 
first two tubes. 

I. Introductory. 

THE multi-stage electron tube amplifier such as is frequently used 
in radio practice and laboratory experiment is essentially an 
instrument for giving a relatively strong response, in the form of an 
electric current or a sound, to a relatively small alternating voltage 
impressed on its input terminals. It is of basic importance to be able 
to describe the behavior of an amplifier, or in other words, to be able to 
predict how a given amplifier will act under given conditions. The 
behavior of an amplifier depends upon the manner in which it reacts 
upon the external input circuit and upon the actions which take place 
inside itself. The general problem, then, of investigating the behavior 
of an amplifier requires the consideration of two interrelated problems, 
the first being the determination of the reaction between the amplifier 
and the external input circuit, the second being the determination of the 
action of the amplifier itself. The first we term the problem of input 
impedance^ the second the problem of detecting efficiency. 

To emphasize the importance of distinguishing between the two phases 
of the general problem let us consider a specific example. Suppose it 
were required to compare two different amplifiers. To do this it would 
seem sufficient to listen by means of them to a steady signal, connecting 



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nSt^^^I detecting efficiency of electron tube. 275 

each one in turn to the same circuit. Such a procedure, however, would 
not in general give a fair test. It may happen that the first of these 
amplifiers, say A , is equivalent to a capacity in series with a large resis- 
tance and gives a large change in the output plate current for a small 
input E.M.F.; while the second, say B, is equivalent to a capacity in 
series with a small resistance but gives a much smaller change than A 
in the output plate current for the same input voltage. If then the test 
were performed on a receiving circuit having a low resistance and capacity 
B would not influence the antenna current appreciably while A would 
decrease it on account of a large input resistance. The decrease might 
be so large that the rectification in the plate circuit might be less with 
A than with B, Thus the test would be in favor of B. If the same test 
were performed on a high resistance circuit the amplifiers being connected 
across a large capacity, then neither amplifier would affect the currents 
in the receiving circuit appreciably. Hence, since A gives a larger recti- 
fication for the same input voltage than B, the test will be in favor of A. 
It is thus seen that an intelligent choice between the two amplifiers cannot 
be made unless both phases of the problem have been solved. 

2. The Input Impedance Problem. 

Let us suppose that the grid and filament of the first tube of an amplifier 
are connected to a circuit in which high frequency current is flowing. 
This circuit is known as the input circuit. In general it is not legitimate 
to assume that the current in the input circuit is the same as it is if 
the amplifier were absent even though there may be no direct inductive 
coupling between the input circuit and the various internal circuits of 
the amplifier. The problem of unravelling the factors which enter into 
this effect is termed the input impedance problem. 

This question has been discussed by H. W. Nichols^ and by J. M. 
Miller.^ They showed that the effect of a single tube, when the grid 
current is zero, is equivalent to that of an electric circuit having a definite 
resistance and reactance which was calculated. In a paper* by one of 
us the single electron tube has been dealt with for the cases of positive 
and negative grid voltage, and the exact formulas have been worked out. 

Thus, the problem of the input impedance is considered to have 
received a complete theoretical solution for the case of a single tube. 
The more complicated case of the multistep amplifier has as yet not been 
treated theoretically, although it would appear that the problem offers 
no fundamental difficulty. 

> Phys. Rev., 13* 404. 1919. 

* Bureau of Standards Scientific Paper* No. 351. 

* '*The Calculation of Detecting and Amplifying Properties of an Electron Tube from its 
Static Characteristics," G. Breit. (As yet unpublished.) 



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276 



JS. 0. HULBURT AND G. BREIT, 



fSSCOND 

LSbkhs. 



3. The Detecting Efficiency of the Amplifier. 
The main purpose of the present work was the consideration of the 
second phase of the general amplifier problem, namely, the detecting 
efficiency of the amplifier. The detecting efficiency of the amplifier 
means, in general words, the efficiency of the amplifier to make weak 
signals intelligible. A precise definition of detecting efficiency is given 
later on. From general considerations it can be seen that the detecting 
efficiency depends upon the relation between the input grid voltage 
change and the resulting change in the output plate current. Therefore 
this relation must be determined either by theory or experiment before 
much can be said about the detecting efficiency of the amplifier. To 
determine this relation from theoretical considerations is, however, a 
somewhat difficult matter. Let us point out some of the difficulties 
briefly. Since the relation between the input grid voltage* change and 
the output plate current change depends upon the amplification and 
rectification taking place in each tube, it is necessary to have an accurate 
knowledge of the characteristics of the electron tubes. These character- 
istics must be known with a precision sufficient to enable one to compute 
the first and second derivatives of the plate current and grid current 
with respect to plate voltage and grid voltage, respectively. It is 
further necessary to know the resistance and reactance of all the electrical 
circuits connected to the tubes for all frequencies. If the tube and 
circuit constants have been ascertained, then the output plate current 
can be computed for a given input grid voltage. Since both the measure- 
ments of the constants and the computations in the case of the amplifier 
are somewhat involved it appeared better from an experimental stand- 
point to measure directly the output plate current as a function of input 
grid voltage. 

4. General Experimental Procedure. 

The type of amplifier chosen for investigation was the three tube high 




Fig. 1. 

frequency transformer-coupled amplifier. This amplifier, shown sche- 
matically in Fig. I, may be used to receive modulated radio frequency 



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Nc^4^'*l DETECTING EFFICIENCY OF ELECTRON TUBE, 277 

signals. Apparatus was arranged to investigate the effect on the rectified 
component of the plate current of the last tube of impressing in some 
branch of the input grid circuit a high frequency E.M.F. of the form 
A cos «/, where ^4 is a constant. It is shown in the following paragraph 
that the results obtained from such a procedure are also true for the case 
where A is not a constant but varies in a certain manner. 

Suppose that the frequency of modulation is so low that the reactances 
of the plate and grid circuits are negligible for that frequency. Let 
there be an external E.M.F. impressed in some branch of the circuit 
between Fi and Gi of the form 

^(a)'/)'COs («/ — e), 

where w/t is the radio frequency and w'/^ is the frequency of modulation. 
^ is a periodic function of period 2t, which is supposed to be always 
positive for real values of the argument. If ^(oc) is zero for some real 
value of X the modulation will be said to be complete. If there is no real 
value of X which makes ip{x) zero the modulation is Said to be incomplete. 
Since the reactances of all the circuits are negligible at the frequency 
«72t, it is legitimate to assume that at any instant of time, /o, the plate 
current of the last tube is the same as it would be if an E.M.F. ^(w'/o) 
cos (o)/ — e) had been impressed on the amplifier for an infinite time. 
If such were the case, the plate current would in general be different 
for different values of <p(u>%). Thus it is sufficient to investigate the 
effect on the plate circuit of the last tube of impressing in some branch 
of the input circuit an E.M.F. of the form A cos cat where ^4 is a constant. 

5. Experimental Details. 

The apparatus consisted of a condenser potential divider, the amplifier, 
and a quadrant electrometer connected in the plate circuit of the last 
tube of the amplifier. These will be described in the order named. 
The arrangement is shown schematically in Fig. i . 

In order to impress on the grid of the amplifier a high frequency 
voltage of known amplitude of the same order of magnitude as that 
obtained in the reception of radio signals a condenser potential divider 
was devised. This consisted of three variable condensers of capacities 
Ci, C2, and Ci connected to a coil L in which high frequency current was 
induced by a suitable electron tube generating set. A thermo-gal- 
vanometer A measured the total current through the combination of 
condensers. The amplifier was connected across C2, so that the voltage 
across C2 was Eg, the effective grid voltage of the input tube of the 
amplifier. The high resistance leak Ri (about 2 megohms) was con- 



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278 £. O. HULBURT AND G, BREIT, j^ms. 

nected across Cj to ensure a definite value of Eg during the experiment. 
The eflFect of Ri upon the impedance of d was negligible, because Ct 
was large (about 0.05 fiF) and the frequency used was of the order of 
3 X 10*. If the effective value of the current through il is / and the 
frequency of the current is w/ax, then it may be shown that 



a)(CiC2 + CiC, + GO 



By adjusting Cs to a small value and Ca to a large value the coefficient of 
/ in the above equation may be made so small that a readable value of / 
is obtained when Eg is comparatively small. The absence of stray 
capacity effects was tested by using different condenser settings and 
different values of current. In order to eliminate direct action between 
the generating set and the amplifier, twisted leads about five meters 
in length were used between L and Cu and between Ct and the amplifier. 
This difficulty increases as the number of stages in the amplifier is in- 
creased, but by increasing the distance between the various parts of the 
apparatus it appears to be possible to reduce any direct action sufficiently 
for practical purposes. 

The amplifier was a three-tube high-frequency transformer-coupled 
amplifier. The tubes were Western Electric Company tubes. Type VTi ; 
they were used with the filament current always i.io amperes and the 
plate voltage always 22.0 volts. Separate storage cells supplied each 
filament; the plate voltage supply was common to all the tubes. By 
means of a standard cell B, Fig. i, the input voltage Eg was kept always 
at a standard value. The plate battery was shunted by a 2nF condenser 
C4. The transformers Ti and T2 were resonance transformers, both tuned 
to the same radio frequency. They were made of No. 36 silk-covered 
copper wire wound on paraffined wooden spools 3 cms. in diameter, 200 
turns on the primary and 250 turns on the secondary winding. 

The change in the value of the rectified component of the output 
plate current of the amplifier was measured by a Dolezalek quadrant 
electrometer Q, Fig. i, connected across a high resistance Rt placed in 
the plate circuit. The connections are shown in Fig. i. The sensibility 
of the electrometer was 2500 mm. deflection per volt difference of potential 
between the quadrants. R2 was 60,000 ohms. Therefore the electrom- 
eter deflection in millimeters could be reduced to the plate current change 
in amperes by dividing by 15 X 10^. Pi and P% are potential dividers. 
Pi serving to keep the plate voltage at a standard value, and Pt to 
compensate for the potential drop in the resistance R^, so that the 
electrometer rested approximately at zero. When the input grid voltage 



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Na\?^'l DETECTING EFFICIENCY OF ELECTRON TUBE. 279 

was changed, a deflection of the electrometer resulted which was pro- 
portional to the change in the rectified component of the output plate 
current. 

It was important that the filament voltage of the last tube and the 
voltages of Pi and Pi be constant. Storage cells were found to be suffi- 
ciently steady for the purpose. When a slow drift of the electrometer 
occurred, the error was eliminated by averaging deflections. 

6. Experimental Results. 
The electrometer deflections, which were proportional to the change 
in the value of the rectified component of the output plate current, 
were recorded for a series of values of the amplitude of the radio frequency 
voltage impressed on the input grid for various frequencies. It was seen 
that the electrometer deflection was nearly proportional to the square 
of the amplitude of the grid voltage. This meant that the rectifying 
action of the last electron tube was represented approximately by the 
expansion of the plate-current grid-voltage relation, by Taylor's theorem, 
in which derivatives of higher order than the second were neglected. 
In Fig. 2 are shown the curves for the electrometer deflection plotted 
against the square of the grid voltage for the five different frequencies 
corresponding to the wave-lengths 800, 825, 850, 875, and 900 meters. 

7. The Detecting Efficiency. 
If il ai^d 60 denote the amplitude of the change in the input grid 
potential and in the rectified component of the output plate current, 
respectively, the detecting efficiency for a given frequency is defined 
conveniently by the relation 

detecting efficiency = lim -ji . 

The detecting efficiency for a specified wave-length is obtained from the 
slope at the origin of the curve of Fig. 2 for that wave-length. The slopes 
at the origin have been computed for each curve of Fig. 2, and are shown 
in Fig. 3 plotted as ordinates against wave-lengths as abscissas. These 
slopes are reduced to the detecting efficiency by dividing by 15 X 10^ 
which is the factor of proportionality between electrometer deflection in 
millimeters and the change in the rectified plate current in amperes. 
It is seen from Fig. 3 that the detecting efficiency of the amplifier is 
greatest at wave-length 850 meters. It is to be noted that the results 
shown in Fig. 3 give a complete solution of the question of the numerical 
value of the detecting efficiency of the amplifier. They do not, however, 
give any information as to the various factors upon which the detecting 



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28o 



E. O. HVLBURT AND G. BRBIT. 



[i 



.*rMfflMt_ 



efficiency depends. Nor do they yield information concerning the input 
impedance of the amplifier. 

In order to check experimentally the assumptions of section 4 the 
following test was carried out. With a given current in A, Fig. i, the 



HOO. 



320 



Electrometer 
deflection 
in rr\vr^ 
or 

b.«l5»'^0'aTnps 



2H0. 



160 



80 




"0002 OOOH Q006 0008 >^ 0.010 0.012 volts* 

Fig. 2. 

electrometer deflection was noted. A 500-cycle interrupter was intro- 
duced to chop the exciting current. When the coupling between^the 
generating set and L was increased until the current had its previous 



6000 



MOOD 



2000 



Detecting 
efficiency*l5«IO^ 




800 meters 



850 wave-length qOO 

Fig. 3. 



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Na*4^''l DETECTING EFFICIENCY OF ELECTRON TUBE. 28 1 

value, it was found that the electrometer deflection was the same as 
before. This test was repeated for various frequencies of the interrupter 
with the same result. This showed that modulating the exciting wave 
in the manner described above did not change the detecting efficiency 
of the amplifier. 

8. Amplification of Each Stage. 

The degree to which the detecting efficiency depended on each stage 
of the amplifier was determined by measuring the detecting efficiency 
of the amplifier for wave-length 850 meters with the first tube discon- 
nected and then with the second tube also disconnected. It was found 
that the detecting efficiency of the amplifier with all three tubes was 
proportional to 9710, with two tubes 1020, and with one tube 104- 
The amplification due to the first tube was, therefore {i^ = 9.7 and 
that due to the second tube was Wi^ — 9-^- 

This meant that the square of the radio frequency voltage from filament 
to grid of the second tube was 9.7 times as great as the square of the 
input grid voltage provided that the voltage was sufficiently small. Any 
rectifying action which occurred in the successive stages did not influence 
the result, because the slope of the curve was taken at the origin, and 
rectification is known to depend on terms in AEg of higher order than the 
first. For amplitudes which can no longer be considered as infinitesimal 
the rectification may manifest itself by shifting the operating point 
on the characteristic of each tube and thus changing the amplification 
constant and internal resistance of the tube. This may be the explana- 
tion of the curious bends in the curves of Fig. 2. 

9. Sound Intensity Amplification. 

If a modulated radio frequency signal is received by means of the 

amplifier the kinetic energy of the vibrations of the telephone diaphragm, 

and also the energy of the sound waves produced thereby, is proportional 

to the square of the amplitude of the change in the rectified component 

of the plate current. The amplitude itself is, however, proportional for 

the same input radio frequency voltage to the square of the detecting 

efficiency as defined above. Consequently, for weak signals the sound 

intensity is proportional to the square of the detecting efficiency. In 

the case of the amplifier cited above the sound intensity was increased 

in the ratio of 9 X 10' : i owing to the use of the first two tubes. 

Johns Hopkins Uniyersfty, 
March, 1920. 



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282 K, T, COMPTON, J2. G. LILLY, P, S. OLMSTEAD, fllSI? 



LSBEIBf. 



THE MINIMUM ARCING VOLTAGE IN HELIUM. 

By K. T. Compton, E. G. Lilly. P. S. Olmstead. 

Synopsis. 

Helium Arc; Minimum Arcing Voltage, — The arc was stimulated by an intense 
thermionic current passed between electrodes in very pure helium. 20 voUs was 
found to be a well-defined minimum voltage at which the arc will strike or break, 
although it may be maintained on voltages as low as 8 volts after having struck. 

Helium Spectrum; Voltage for Excitation of Lines and Bands. — ^Apparently the 
ordinary helium and parhelium lines and the bcuids aie excited whenever the arc 
strikes. The line 46S6 of the enhanced system was never observed below 55 volts, 
and was stronger above 80 volts. The lines of the sharp subordinate series of pairs 
are peculiar in that their intensity decreases, relatively to that of the rest of the 
spectrum, as the voltage is increased. 

The results are in accord with Bohr's theory of radiation and atomic structure. 

Introduction. 

RECENT investigations of the production of radiation and ionization 
by electron impacts in helium^ have shown that the minimum 
radiating potential of this gas is close to 20.2 volts and its minimum 
ionizing potential is 25.5 volts. One of the writers has shown* that these 
values apply to radiation and ionization set up by a single electron 
impact against a normal unexcited atom, whereas, if the electron current 
and gas density are relatively large, ionization may occur at any voltage 
above 20.2 volts. This ionization at abnormally low speed is presumably 
due to impacts against atoms which are in a relatively unstable condition 
due either to preceding impacts or to the absorption of radiation coming 
from neighboring atoms which have been struck. The latter of these 
causes is much more important than the former. Neither radiation nor 
ionization has ever been observed below 20 volts. 

These considerations suggest that 20.2 volts should be the minimum 
voltage at which an arc can strike in helium and that the necessary 
conditions for obtaining an arc at this voltage are an intense bombarding 
electron current and relatively high gas pressure, so that the amount of 
ionization due to the comulative effect of impacts and radiation may be 
sufficient to cause an arc. 

Rau' and Richardson and Bazzoni^ have published results of experi- 

^ F. Horton and A. C. Davies, Roy. Soc. Proc A.. 95. p. 408. 1919; Franck and Knipping. 
Phys. Zeit.. 20. p. 481, 1919. 

* K. T. Compton. Phil. Mag. (in print) 

* Sitz. Ber. d. Phys. Med. Ges. zu WQrzburg. p. 20. 1914' 

* Nature, 98. p. 5. 1916. 



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Na"^^'] MINIMUM ARCING VOLTAGE IN HEUUM. 283 

ments on arcing potentials and the arc spectrum in helium. The lowest 
arcing voltage found by Rau was 24.5 volts. This was in the presence 
of mercury vapor, whose ionization increased the current density and 
thus caused the helium arc to strike at a lower voltage than in pure 
helium. Apparently 29.5 volts is the lowest voltage at which Rau 
obtained the arc in pure helium. Richardson and Bazzoni, working with 
helium in the presence of mercury vapor, obtained the helium arc 
spectrum at 22.5 volts, the mercury arc spectrum appearing first at a 
slightly lower voltage. 

The following experiments were made to determine the voltage at 
which the arc strikes under various conditions of gas pressure and 
electron current density in very pure helium. It was found that the 
arc could be made to strike at voltages as low as 20 volts, but never lower. 
Under favorable conditions, however, the arc could be maintained at 
much lower voltages, the lowest voltage observed being 8 volts, with a 
gas pressure of 5 mm. and a current of about an ampere through the gas. 
Observations of the spectrum were also made under various conditions. 

Apparatus. 
The arc was obtained between an incandescent tungsten wire cathode 
and a nickel disk anode, enclosed in a glass bulb. Wires of various 
diameters from 0.06 mm. to 0.25 mm. were used, and their lengths varied 
from I cm. to 2 cm. The distance between the electrodes varied between 
I cm. and 3 cm. in different bulbs. A large bulb of cocoanut charcoal 
was sealed directly to one end of the experimental tube, while to the 
other end was attached the glass tubing connection to the helium reservoir 
and pump. This connecting tube was bent into two U tubes near the 
bulb. The one nearest the bulb was a trap to prevent the entrance into 
the bulb of water or mercury vapors and the further one contained 
charcoal. The bulb and the charcoal tubes were baked out in an electric 
furnace maintained at a temperature between 300** and 350** C. for several 
days while the apparatus was evacuated by a diffusion pump. Liquid 
air was then applied to the trap and later to the two charcoal tubes 
before the helium gas was admitted. A mercury hand pump with a 
magnetically operated valve permitted the gas pressure to be adjusted 
to any value between o and 24 mm. A Hilger wave-length spectrometer 
was used for the examination of the spectrum. In every case observa- 
tions were made at increasing filament temperatures until the wire burned 
out. The voltage across the arc and the current through it were regulated 
by series and parallel resistances connecting it to a no volt storage 
battery. 



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284 



K. T. COMPTON, E. G. LILLY, P. S. OLMSTEAD. 



rSscoND 
ISbkizs. 



Results. 

From among the large number of sets of observations made only a few 
examples can'be given in the accompanying figures. Possibly the results 
can be most concisely presented by discussing them under the four 
following cases, which are somewhat arbitrary and not always mutually 
exclusive. 

Case I. — No arc* The current increases as ionization and radiation 
set in above 20 volts, but there is no discontinuous change or visible 



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radiation. Variations of current with voltage are reversible. This case 
is observed at any gas pressure if the thermionic current is small and 
with any thermionic current if the gas pressure is small. Example: 
Fig. I. 

Case II. — The arc strikes at a voltage above about 29 volts and breaks 
at a voltage above 20 volts. There is no characteristic value for either 
the striking or breaking voltage, since they may be varied by varying 
the thermionic current or pressure. In general any change which in- 
creases one, also increases the other. The arc current always increases 
as the applied voltage is increased, but there is a region of irreversible 
changes between the striking and breaking voltages. Example: Fig. 2. 

Case III, — The arc strikes at a voltage below 29 volts and breaks at 
20 volts. Here it is found that, by increasing the thermionic current by 
raising the filament to a higher temperature, the striking voltage may 
be reduced as low as 20 volts, but the breaking voltage stays constant 



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Vol. XVI.l 
No. 4. J 



MINIMUM ARCING VOLTAGE IN HELIUM. 



285 



at 20 volts. Between the striking and breaking voltages the current- 
voltage changes are irreversible. Example: Fig. 3. 

Cfise IV. — ^The arc strikes at 20 volts and breaks at 20 volts, although 
it may be maintained at lower voltages if the current of the arc is in- 
creased by decreasing the series re- 
sistance. But no further increase in 
the thermionic current will cause the 
arc to strike or break at voltages 
below 20. This seems, therefore, to 
be a definite minimum value for the 
arcing voltage — and, therefore, for 
the excitation of the spectrum. If, 
after the arc has struck, the series 
resistance is decreased, the current 
increases and the potential drop 
across the arc decreases. In one 
case the arc was thus maintained on 
8 volts and in another case on 10 
volts. There seems to be no lower 
limit for the maintenance of the arc, 
once it has struck, for this seems to 
be limited only by the size of the 
currents which the electrodes will 
carry. In every such case, as the series resistance is again increased, 
the voltage again rises to 20, where the arc breaks. Example: Fig. 4. 

There are several interesting peculiarities of the arc which have been 
noticed during the experiments. Between Case III. and Case IV. 
there is an intermediate condition which may be considered as marking 
the division between them. Here the arc strikes at 20 volts, and remains 
at 20 volts however the current through the arc be increased by decreasing 
the series resistance. In this condition the resistance of the arc varies 
exactly inversely with the current through the arc. In one case the 
current between the electrodes was varied at will from 50 microamperes 
to 50,000 microamperes without producing any variation in the potential 
drop of 20 volts. 

The current and voltage of the arc, with large currents, often exhibited 
discontinuous changes as the geometrical distribution of the arc in the 
tube suddenly changed. As far as we could tell, these shifts gave no 
indication of critical voltages in addition to that at 20 volts, since they 
seemed to be more or less accidental and occurred at different voltages 
at different pressures and with different positions and shapes of the 
electrodes. 



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286 



K. T. COMPTON. E. G. LILLY, P. 5. OLMSTEAD. 



rSsCOND 

LSbkhs. 



It should be stated that the observed critical voltage which we have 
called 20 volts, in reality was sometimes as high as 20.5 volts and some- 
times as low as 19 volts. These variations, however, are accounted for 
by the average initial velocities of emission of electrons from the filament 
at the temperatures used. 

In securing an arc under the conditions of Case IV., the optimum gas 
pressure was between 4 mm. and 10 nmi. Higher gas pressures would 
be advantageous, because of the greater probability of ionization by 

500r 



400 
800 
900 
100 


0.1 

^"^0 5 ~iO" ^15 ~20 IF 

Volts 

Fig. 4. 

cumulative impacts, if it were not for the fact that, at such high pressures, 
the electrons make so many collisions in their zig-zag course that the 
aggregate amount of energy which they lose as a result of the momentum 
imparted to the atoms becomes considerable.^ Thus, at the higher 
pressures, voltage greater than 20 volts must be applied in order that 
the electrons may acquire a velocity corresponding to 20 volts. 

Spectroscopic Observations. 

As far as we could tell, the entire helium spectrum, with the exception 
of the enhanced lines, appeared whenever the arc struck, and therefore 
1 Benade and Compton. Phys. Rev., ii, p. 184, 1918. 



^^^^^ 


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f 


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No!"^^^*l MINIMUM ARCING VOLTAGE IN HELIUM. 287 

appeared at potential differences as low as 20 volts. This was ap- 
parently true of the band as well as of the line spectrum, although the 
relative faintness of the bands made it impossible to see them at voltages 
quite as low as 20. With the most intense arc, the lowest voltage 
at which the bands were observed was 26 volts, but the indications 
were that we missed them below this voltage because of lack of intensity 
rather than because they were not excited. The most prominent 
line of the enhanced spectrum is the first member 4686 of the series 
4iV[(i/32) — (i/m^)]. Rau was able to excite this line only with potential 
drops of 80 volts or more. At gas pressures of less than about 3 mm. 
and with thermionic currents not too intense, we have found that this 
line suddenly appears as the voltage is raised above 80 volts, but, with 
more intense currents and pressures between 3 mm. and 5 mm., the line 
may be seen at voltages as low as 55 volts. In these cases, however, the 
intensity of the line considerably' increases if the voltage is raised above 
80 volts. At still higher gas pressures, such as 10 mm., we were unable 
to excite this line at any voltage used. 

We verified Rau's and Richardson and Bazzoni's observations that 
the line 4713, which is the second member of the sharp subordinate 
series of the system of pairs, decreased in intensity with increasing 
voltage, although the lines of the other series increased strongly. We 
observed this also in the case of the first member 7066 of the same series. 

Although the band spectrum was excited at apparently the same 
voltage as the rest of the arc spectrum, it appeared that it was relatively 
most intense at high gas pressures, from 10 mm. up. At these pressures 
we observed the bands noted by Fowler^ very easily, and, in addition, 
some fainter bands. One of these consists of two or more sections 
extending from about 5748 to 6044. Another seems to consist of six 
pairs, equally spaced, between 5719.5 and 5657. There is another set 
of fine lines beginning at about 4575 and extending to 4378, with evidence 
of the convergence of a series at the latter wave-length. We are some- 
what hesitant about mentioning these, since our spectroscopic equipment 
was not sufficiently elaborate to permit of refined observations, and 
yet we are unable to attribute them to an impurity, since the gas seemed 
to be very pure. There was no trace of the spectra of mercury, other 
inert gases (with the possible exception of neon) or of hydrogen (except 
in the case of one bulb on which a quartz window was waxed and which 
could not be given adequate "baking out")« Several of the faint lines 
of these bands corresponded, within the limits of accuracy of our observa- 
tions, with certain neon lines, but there was no trace of the three or four 
strongest neon lines in this region, or elsewhere in the spectrum, at pres- 

* Roy. Soc. Proc. A, 91, p. 208, 191 5. 



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288 K. T. COMPTON. E. G, LILLY, P. 5. OLMSTEAD, [^ 



sures at which the bands were prominent, and there was no uniformity 
between the neon spectrum in general and the observed spectrum. 

Discussion. 

The results of this investigation confirm the view that ionization 
may occur at any voltage above the resonance potential as a result of 
the impact of an electron against an atom which is already partially 
ionized through the absorption of a quantum of resonance radiation 
from neighboring atoms. In other words, the presence of resonance 
radiation changes the condition of the atom to one of easier ionization. 
In the intense arcs in which the discharge was maintained far below 20 
volts, it is evident that practically all the atoms were in an abnormal, 
easily ionizable, condition. We may picture the state of affairs as one 
in which an electron, returning toward its normal most stable position 
step by step, and radiating energy at each step, is again partially or 
entirely ejected towards less stable positions by absorption of radiant 
energy or by impact before it has an opportunity to return to the most 
stable position. Thus the bulb contains a large density of radiant energy 
of various spectral frequencies and helium atoms in all stages of ionization, 
or degrees of stability. The more intense the arc, the larger is the pro- 
portion of atoms whose electrons are in the outer orbits, or least stable 
configurations, so that the arc may be then operated on reduced voltage. 
The first step, however, essential to reaching this condition and the 
excitation of visible radiation, is the displacement of the electrons from 
their most stable to their next most stable configuration — a displacement 
requiring an amount of energy which is acquired by an electron in falling 
through 20 volts. 

The investigations of low voltage arcs in mercury and other metallic 
vapors^ are to be interpreted in a similar way. In every case the arc 
may be made to strike at a voltage equal to the resonance potential, 
and may be maintained at a lower voltage. Here, however, the voltages 
are low, so that the initial velocity distribution of the electrons from the 
filament introduces uncertainties of a relatively large magnitude as 
compared with those in the present case. By analogy with these metallic 
vapors, we should expect to find a very strong emission series in helium, 
with the first member (also an absorption line) at about 605 A. and con- 
vergence at about 484 A., corresponding to 20.2 volts and 25.5 volts. 

The theories of atomic structure, which are rather uncertain with 
regard to the constitution and radiation of ^stems with more than one 
electron, have been quite successful in accounting for the spectra of 

1 McLennan. Phys. Soc. Lond. Proc., 31, p. i, 1918; Hebb., Phys. Rbv., 9, p. 37a. 1917; 
II, p. 170, 1918; 12. p. 48a. 1918 and others. 



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No^4?^''] MINIMUM ARCING VOLTAGE IN HELIUM. 289 

atoms With a nucleus and a single electron. On Bohr's theory, the 
spectral series from helium atoms which have lost one electron should 
be given by the formulae 

whence the negative energies of the various configurations of an electron 
are given by ^N/n^, where n may have various integral values from i to « . 
Thus the energy required to change the electron from its most stable 
to its next most stable condition is 4iV(i/i* — 1/2*), or 3iV; while the 
energy required to completely remove it is 4N. The minimum energy 
required to change the electron from the most stable condition to that 
condition in which it may emit the line 4686 is 4iV(i/i* — 1/4*) » or isNf^. 
Thus the energy, in equivalent volts, required to remove the second 
electron from an atom already ionized, is 54.3 volts, while the energy 
required to cause such an atom to emit the 4686 line corresponds to 
50.8 volts. Similarly, the minimum energy required to cause an atom, 
originally neutral and normal, to emit this radiation corresponds to 
50.8 + 25.5 = 76.3 volts; that required to cause an atom which has 
absorbed a quantum of the resonance radiation to emit this line corre- 
sponds to 76.3 — 20.2 = 56.1 volts; that required to doubly ionize an 
atom at a single impact is 25.5 + 54.3 = 79.8 volts if the atom is origi- 
nally normal and is 79.8 — 20.2 = 59.6 volts if the atom has absorbed 
resonance radiation. 

There are thus various ways in which the 4686 radiation may be 
excited. Of these, the excitation by a single impact at 79.8 volts or more 
should predominate at low pressures and currents, while at higher 
pressures, with most of the atoms in the abnormal state, the excitation 
should be caused by 56.1 volts or possibly even by 50.8 volt impacts. 
These possibilities accord with our observations, in which the 4686 
line was observed at voltages as low as 55 volts in a very intense arc, 
but with evidence of another method of excitation at 80 volts which was 
relatively more important at low pressures and arc intensities. The 
failure to observe the line at pressures above 10 mm. is evidently due 
to the very small chance of the electrons falling through a sufficiently 
large potential difference without losing their energy at an ionizing or 
radiating impact. 

The fact that the lines of the so-called Parhelium series appear at the 

same voltages as those of the Helium series renders untenable Stark's 

conclusion that they are due to atoms which have lost more electrons 

than those atoms which give rise to the helium series lines. 

PALBfBR Physical Laboratory, 
Princeton University. 



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290 HAROLD F. RICHARDS. IsJSS 



ELECTRIFICATION BY IMPACT. 

By Hakold F. Richakds. 

Synopsis. 

EUctrificaiion by Impact; Measurement of the Charge Produced by Collision 
between a Metal and a Dielectric. — ^After briefly discussing the unsuccessful attempts 
which have been made to formulate a satisfactory theory to explain electrification by 
friction, the author suggests that impact of dielectric upon metal, without sliding 
friction, may cause an electrical effect whose laws will shed light upon the frictional 
phenomenon. An apparatus is described for measuring the electric charge produced 
when a disc or sphere of dielectric material collides with a metal disc. The charges 
obtained in this manner ranged from 0.16 to 9.83 e.s.u., and produced potentials of 
2.41 to 183.8 volts upon the metallic sj^tems employed. These charges are of the 
same order of magnitude as those obtained by friction. The experiment was 
performed with various metals and dielectric^, and in every instance the metal received 
a positive charge. In no case was there any evidence of the erratic variation which 
others have found to be characteristic of electrification by friction. Curves are 
given which show the variation of charge with velocity of impact and with the mass of 
the impinging system. The charge produced by a single collision increases with each 
of these factors, but the velocity of impact was found to exert a greater influence 
than the mass of the moving body, in determining the amount of the charge. In 
certain cases velocities were attained at which the electrification due to a single 
impact reached a maximum value. 

Relation of Charge to Capacity, — The quantity of charge produced by a given 
collision was shown to be independent of the capacity of the metallic system. 

Effect of Repeated Impacts. — ^When many impacts were performed in rapid 
succession, the amount of charge increased to a maximum. This maximum was 
shown to be conditioned rather by the quantity of charge present upon the dielectric 
than by the potential of the metal anvil. 

Discussion of Results. — The author concludes that there is no direct dependence 
of the electrical energy upon the mechanical energy lost in impact, and that electri- 
fication by impact is similar in nature to the contact effect between metals. The 
results are considered to support Helmholtz's theory regarding the nature of 
electrification by friction. 

I. Introduction. 

THE very meager quantitative results and theoretical study of 
electrification by friction have prevented the formulation of a 
satisfactory theory to explain the phenomena involved. Perhaps the 
most important work in this field is that of Owen,^ who finds many 
indications that the effect is similar to the contact difference of potential 
between metals, thus agreeing with Helmholtz.^ The latter had pre- 
viously suggested that the function performed by the frictional work is 

» Phil. Mag., XVII., p. 457 (1909). 

« Wissenschaftliche Abhandlungen, Erster Band. p. 860. 



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Na"^^^*] ELECTRIFICATION BY IMPACT. 29 1 

merely to bring the molecules of the two substances into closer contact. 
Owen concludes that, with a sufficient amount of frictional work, the 
charge reaches a constant maximum, and that this maximum is attained 
with a smaller amount of work the greater the pressure between the 
rubbing surfaces. He notes further that less work is required to produce 
a given charge if contact is improved by a series of rubs. Jones,^ how- 
ever, definitely rejects these views, as is shown by the following quotation 
from his paper: '* Frictional electricity appears, therefore, to be an effect 
of a different order from that of contact electricity, and it is worth while 
considering whether the facts cannot be accounted for on some other 
hypothesis." He assumes that the rate of production of charge is pro- 
portional to the rate at which work is performed, and explains the fact 
that the charge reaches a maximum value by assuming that back-leakage 
occurs in an amount proportional to the total charge present. It is 
difficult to see how this theory can account for the fact that one substance 
remains positive with respect to another, a phenomenon which is readily 
explained by the theory of Helmholtz. Thus, in spite of attempts to 
formulate a consistent theory, no great success has been attained, 
because the data of electrification by friction remain essentially erratic. 
This is abundantly shown by the experiments of Owen and Jones, and 
also by the later work of French* and McClelland and Power,* who 
find that not only the amount, but even the sign, of the charge varies 
with the conditions to which the rubbing surfaces are exposed before 
an experiment. 

The present work was therefore undertaken to find what electrical 
effect would be produced by intimate contact, without friction^ between 
metals and dielectrics. Both Owen and Jones have found that mere 
contact of such substances does not produce a detectable amount of 
electrification, but it is probable that the contact in their experiments 
was not such as would bring the surfaces sufficiently close together to 
furnish an adequate test. It was my belief that the more intimate 
contact produced by collision might cause an effect whose laws would 
shed light upon the nature of electrification by friction. It seems 
evident that the more definite nature of a single impact at a known 
velocity will give to the data of such an effect a greater consistency 
than that which characterizes the results of electrification by friction. 

> Phil. Ma«.. XXIX.. p. 272 (191S). 

*Phys. Rev.. IX., No. 2. p. 151 (1917). 

•Roy. Irish Acad. Proc. 34, Sect. A, p. 40 (1918). 



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292 



HAROLD P. RICHARDS. 



rSBCOND 

LSI 



2. Apparatus. 
The apparatus used in the first experiments is indicated in Fig. i. 
An ebonite disc E fits firmly into a brass socket attached to the lower 
end of a brass tube A sliding in a cylinder D. A is 2.5 cm. outside 
diameter, 17.5 cm. long, while D is 3.1 cm. inside diameter and 35 cm. 
long. The sliding tube is provided with studs to form a three-point 
contact at top and bottom, and these were carefully machined so as to 
permit free fall with minimum lateral freedom. Uniformity in bore of 
the stationary cylinder, the low-friction close-fitting contact of the 
bearing studs, arid the relatively large ratio of the length of the falling 




Fig. 1. 



tube to its diameter, all combined to ensure uniform orientation of the 
ebonite surface at the moment of impact with a brass disc B. The 
latter was fastened securely to an ebonite pedestal P by means of a 
threaded projection of its own material. The pedestal was firmly held 
in a heavy iron base. All the horizontal surfaces were rendered parallel 
by careful turning in a lathe. An index rigidly attached to the plunging 
cylinder indicated the height of its fall. The air space between the 
cylinders provided windage, but windows were also constructed at the 
base of D to prevent compression of air. F is an earthed metal cylinder. 
The ebonite and brass discs were each 2.5 cm. in diameter, and of a 
thickness of 0.95 and 0.32 cm., respectively. 

The charge produced upon the metal disc was measured by means of a 
Wilson tilted electroscope W, which was chosen on account of its low 



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Na*4?^^*] ELECTRIFICATION BY IMPACT, 293 

capacity (2.3 cm.), and consequent high sensitivity to quantity of charge. 
Deflections were observed with a microscope containing a micrometer 
eyepiece. The plate of the Wilson electroscope was maintained at a 
constant potential of 140 to 180 volts by a battery of accumulators, 
and the sign of this potential was always kept the same as that of the 
charge to be measured, so that the instrument was used in its most stable 
condition. The scale of the microscope contained 40 divisions, and the 
position of the goldleaf could readily be estimated to o.i division. 
Calibrations made with multiples of Weston standard cells furnished 
ciuves showing the voltages corresponding to given deflections. Various 
sensitivities were used, ranging from 3 to 10 divisions per volt, and for 
these values the deflections were nearly, but not quite, proportional to 
the potential of the goldleaf. Accurate adjustment to the desired 
sensitivity was obtained by the use of a potentiometer arrangement, 
indicated at R. Under the conditions described, the Wilson electroscope 
furnished a most convenient and satisfactory means of measuring the 
charges produced by impact. The metal disc and measuring apparatus 
could be earthed or insulated either together or separately, by means of 
a double key K operated by a simple arrangement of two strings. Care 
to prevent leakage was taken and, in addition, all charged portions of the 
apparatus were housed in earthed metal boxes for electrostatic protection. 

3. Measurement of Capacity. 
The capacities used in these experiments were so small that they 
were measured by comparison with a specially-constructed condenser 
of concentric cylinders possessing a capacity of the same order. The 
dimensions of the inner tube were 2.70 cm. outside diameter and 43.15 
cm. length; the outer cylinder was 4.45 cm. inside diameter and 52.50 
cm. long. As the length compared to the space between the cylinders 
was large, the ordinary formula for capacity can be used. The calculated 
capacity proved to be 43.23 cm. (electrostatic units). All values of 
capacity used in the experiments were determined by comparison with 
this condenser. The capacity of the system was altered whenever 
necessary by inserting in the circuit an adjustable parallel-plate conden- 
ser, whose range of capacity was from 33.9 to 346.1 cm. The sliding 
plates of this condenser were earthed, and the plates receiving the charge 
were mounted rigidly on sulphur pedestals. 

4. Experimental Results. 
A. Variation of Charge with Velocity of Impact, 
The surfaces of the brass and ebonite impact discs were made as flat 
and smooth as possible, and mounted so as to be parallel at the moment 



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294 



HAROLD P. RICHARDS. 



fSlCOMD 
LSutlBS. 



of contact. The cylinder, carrying the ebonite disc, was loaded with 
lead shot to give a total weight to the falling system of 753.8 grams. The 
ebonite disc was raised to various heights by means of a string passing 
over a light pulley, and then released by a mechanical trip so as to fall 
freely upon the brass anvil. The index indicated that there was no 
rebound, and therefore only a single impact. The ebonite was then 
raised 20 cm. above the brass disc and the charge on the latter measured. 
Tests showed that the charged ebonite plunger was sufficiently distant 
to produce no appreciable inductive effect upon the measuring system. 
Between successive impacts the ebonite surface was discharged by 
means of radium. Velocities of impact were calculated from the observed 
distances of fall. 

A single curve was obtained as follows: Three readings were taken at 
each selected velocity when the height of fall was successively increased, 
and then the run was repeated with decreasing velocities. The charge 




to SC JO 70 

VtLOciTY OF Impact in ens per second 
Fig. 2. 

produced at a given velocity was then calculated from the six readings 
of the ascending and descending series, and this average was plotted. 
The charges obtained at a given velocity usually increased slightly after 
repeated impacts, probably due to further flattening of the surfaces, and 



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NoV^^^*] ELECTRIFICATION BY IMPACT. 295 

the effect of this small secular variation was eliminated by averaging 
together the ascending and descending runs. The usual variation from 
the mean in a series of observations at a single velocity was 3 per cent. 
No especial care was taken of the surfaces other than an occasional 
cleansing with alcohol. This treatment made only a small difference, 
usually increasing the charge by a small amount and rendering consecu- 
tive readings slightly more consistent. Upon one occasion cleaning the 
ebonite with a fine, flat file increased the charge from 0.54 to 0.99 e.s.u., 
but, in a velocity run immediately following, the charge reverted to its 
former value. 

The curves exhibited in Fig. 2 show the charges obtained with a single 
impact at various velocities. These representative curves were selected 
from observations extending over a period of a month or more, during 
which many hundreds of collisions were produced between the same 
surfaces. It is seen at once that impact produces charges of the same 
order as those obtained by friction. These charges were of sufficient 
magnitude to raise the brass disc to fairly high potentials. Even the 
relatively low maximum charge shown in Curve II produced a potential 
of 9.75 volts upon the metallic system, whose capacity was 19.9 cm. 
(2.21 X io~' microfarads). The curves show a steady secular increase 
in the charge obtained at a given velocity, and also that, in the early work, 
when the surfaces were fresh, a maximum was attained at the velocities 
used, whereas no maximum was reached in the later experiments with the 
same surfaces. It may be supposed that this is due to increase in the 
contact-area, inasmuch as many collisions would render the ebonite 
surface more nearly plane. 

It is worthy of note that the ebonite disc always produced a positive 
charge upon the brass anvil. There was no tendency towards the 
reversal of sign observed when charge is produced by friction. Even the 
slight residual charge obtained when the dielectric was lowered upon the 
metal with as nearly zero-velocity as possible was always positive, even 
when in amount it was not more than 0.02 e.s.u. 

B. Relation of Charge to Capacity » 
An exhaustive series of experiments was performed to find the relation 
between the capacity of the metallic system and the charge produced 
upon it by a given impact. The variable condenser was adjusted so 
that the charge due to a single collision gave a convenient deflection. 
Three readings were taken when the charge was formed at the capacity 
of the whole system, then three readings when the capacity of the measur- 
ing system was not added until after the impact had taken place. This 



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296 



HAROLD F. RICHARDS. 



com 



process was repeated a number of times in close succession, the charge 
being formed alternately upon the metal anvil and upon the whole system, 
but always measured at the same capacity. The velocity of impact 
remained constant throughout. Thus the only variable was the capacity 
at moment of production of charge. The mean charges found in four 
such experiments are given in Table I. 

Table I. 



Bzperiment No. 


Velocity of Impact 

(cm./iec.). 


Capacity at Impact (cm.). 


Charge (e.t.tt.). 


1 


67.1 
62.6 
70.0 
62.6 


r 19.2 
1 152.5 
f 19.2 
1134.9 
r 123.2 
L 168.8 
1 00 
\ 168.8 


f 1.42 
11.43 
f 1.98 
11.97 
12.22 
12.23 
f 1.04 
11.02 


2 


3 


4 





In order to employ infinite capacity the metal disc was earthed at the 
moment of impact, but insulated before the ebonite disc was raised. 
It had previously been found that the potential of the system was not 
altered until the dielectric was lifted. 

These results show that the charge is independent of the capacity. 
On account of the important conclusions which can be drawn from this 
fact, the observations for one experiment are given (Table II.). Readings 
were taken alternately at the two capacities. 

Table II. 



Capacity at Impact. 


Volts. 


Mean Charge. 


19.2 


2.77 
2.78 


2.82 
2.84 


2.85 

2.85 


2.88 
2.91 


2.83 
2.87 


mean 2.83 
mean 2.85 


1.42 


152.5 


1.43 



C. Influence of Mass of the Plunging System. 
Fig. 3 shows velocity curves obtained in the same manner as previously 
described. The ordinates are the potentials produced by a single impact 
at the capacity of 133.3 cm. The run represented by curve B imme- 
diately followed .4, the mass of the impinging system being decreased as 
indicated. Runs C and £, and G and F, were performed similarly. For 
the smaller mass, the charge is seen to be more nearly proportional to 
the velocity, and there is not the tendency to approach a maximum 
shown by the curves for greater mass. The curves show that a mean re- 



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Vol. XVI.! 
No. 4. J 



ELECTRIFICATION BY IMPACT. 



297 



duction in weight of 48 per cent, produced a mean decrease in charge of 
only 16 per cent., for constant velocity of impact. 

D. Effect of Repeated Impacts. 
Experiments were performed with repeated impacts in order to deter- 



12 

o 

>2 



Cbonitc Disc on A^ass 

C 707 

r 397 


^-^-^ 


^ 


/: 


^ 


^ 

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^ 


^ 







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VrLOC/rr or Impact in cms pzr sec 

Fig. 3. 



100 



mine whether there is a maximum potential or a maximum charge 
obtainable by collision. Fig. 4, Curve I., shows the results when the 









i 



NUMOCR OF I fi PACTS 
Fig. 4. 



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298 HAROLD F. RICHARDS. [ISSS? 

ebonite surface was not discharged between successive impacts. Four- 
teen collisions at a constant velocity of 62.6 cm./sec. could be produced in 
one minute. Insulation was excellent, so that leakage during the largest 
number of impacts was nearly negligible and could readily be allowed for 
by a small correction. The curve shows a maximum charge of 9.78 
e.s.u., which produced a potential of 165. i volts upon the metal disc. 
The charge was shared with a larger capacity for measurement. Then 
the ebonite disc, initially uncharged, was allowed to make five impacts 
upon the brass anvil, which was charged to various potentials by means 
of accumulators. The results are given in Table III. 

Table III. 





Velocity of Impact (cnu/iec). 


Initial Potential of Bnss DIm; 
(Volts). 


Charge Added by Fire Impacts 

(e.s.u.). 


62.6 
62.6 
62.6 


280.2 
350.2 
386.0 


3.31 
3.42 
3.09 



There is seen to be no indication of a limiting potential, at the voltages 
used. It is thus evident that the limiting factor is not the potential of 
the metal anvil, but the amount of charge present upon the dielectric. 

E. Effect of Static Pressure. 
It has already been mentioned that a charge of approximately 0.02 
e.s.u. was always produced when the ebonite disc was lowered upon the 
brass anvil with as nearly no velocity as possible. To determine whether 
greater pressure would increase this charge, weights ranging from 4.38 
to 12.08 kilograms were placed upon the ebonite disc while it rested 
upon the brass. No increase in charge was observed. 

5. The Hurling Experiments. 
A. Apparatus, 
In order to perform the experiments under widely different conditions, 
an apparatus was devised for projecting a sphere of dielectric upon an 
insulated metal disc. The construction is indicated in Fig. 5. A weight 
P falling upon the short end of a light, rigid oak lever L imparted a high 
velocity to a small brass tube H sliding in a heavy sleeve. The rise of 
the sliding tube was small, its motion being suddenly arrested by the 
abutments shown. The pole of the electromagnet M was provided with 
a collar A of non-magnetic material, in order to ensure uniform release 
of the projectile without lateral motion. The ball of dielectric rested 
in the smoothly beveled edge of the sliding tube. A calibration curve 



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Vol. XVLl 
No. 4- J 



ELECTRIFICATION BY IMPACT, 



299 



was obtained showing the maximum free rise of the ball for different 
distances traversed by the falling weight. The action of this hurling 
device was constant to such a degree that the maximum variation from 
the mean in a series of flights was only i .5 per cent, at the highest veloci- 
ties used. The velocity of the ball at a given height h could readily be 
calculated fom the formula v = ^2g{H — A), where H is the maximum 
flight for the drop used. The ball could be projected vertically, so as 
to be pocketed in the hurling cup upon rebound, although in practice 
the ball was received upon heavy lead foil spread a little to one side of 




MUKLIN6 CUP 



Fig. 5. 

the sliding tube, and then rolled into the cup. The metal disc upon 
which the ball impinged was attached to an ebonite pedestal E inserted 
in a massive wood cylinder. C is a metal cylinder to afford electrostatic 
protection. The charge received by the disc was measured in the 
manner previously described. The capacity of the metal disc and its 
connecting wire was 16.0 cm. 

B. Variation of Charge with Velocity, 
Fig. 6 exhibits specimen curves showing the charge produced at various 
velocities by a single impact of ebonite upon brass. The dielectric 
sphere was 2.5 cm. in diameter and had a mass of 10.88 grams. The 
brass disc was 5.0 cm. in diameter by 0.32 cm. thick, and possessed a 
fairly high polish. The flight of the ball through the air before collision 
occurred was 11.6 cm. Discharge of the ball was effected before every 
impact by passing it rapidly through a flame, as it was found that the 
results were not affected by substitution of this agent for radium. Each 



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300 



HAROLD P. RICHARDS. 



fSlOOMD 

iSnuBS. 



point on the curve is the mean of five or six observations at the velocity 
indicated. The maximum variation of a single reading from the mean 
was 8 per cent. As in the experiments with the plunging ebonite disc, 
the initial curves show that the charge reaches a maximum for certain 
velocities, whereas later work indicated that a much higher velocity 
would be required to produce a maximum. A possible explanation for 
this is that after a large number of impacts the ebonite surface was 









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Fig. 6. 

slightly bruised and flattened, although the brass showed no signs of wear. 
The surfaces of the dielectric and metal received no especial care other 
than an occasional cleansing with alcohol. No reversal of sign of the 
charge was ever observed; the charge on the brass was positive for all 
velocities and at every trial. 

C Repeated Impacts. 
Fig. 4, Curve II., shows the charge produced by a given number of 
collisions at a velocity of 179.8 cm./sec. The ebonite ball was discharged 
between impacts. Seven collisions could be effected in one minute, and 
leakage during the time required for the largest number of impacts was 
nearly negligible, so that only a small correction was necessary. Twenty 
impacts produced a potential of 183.8 volts upon the brass disc. The 
curve shows that there is a tendency towards a maximum, although the 
dielectric was discharged between impacts. This result differs from the 
conclusion based upon the data given in Table III. for a similar experi- 
ment with the ebonite disc. The reasons for this will be discussed later. 



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Vol. XVI.1 
Na4. J 



ELECTRIFICATION BY IMPACT, 



301 



D, Various Metals and Dielectrics. 
Tests were made when a zinc disc was substituted for brass, and a 
glass ball for ebonite, the results of which are shown in Table IV. The 
charge is due to a sing!e impact. The zinc disc was 5.0 cm. in diameter 
and 0.5 cm. thick. The glass sphere had a diameter of 1.9 cm. and a 
mass of 8.23 grams. 

Table IV. 



Materials. 

Ebonite on brass . . . . 

Ebonite on zinc 

Glass on brass 

Glass on zinc 



Coeflcient of 
RetUtncy 



0.74 
0.70 
0.40 
0.30 



Valodty of Impact 

(cm. /tec). 



292.0 
166.8 to 252.8 
200.0 to 285.9 
200.0 to 246.5 



Charge (e.s.a.). 



1.37 
0.87 
0.57 
0.81 



In every instance the metal received a positive charge. An ivory ball 
also produced a positive charge on brass. In all cases except that of 
ebonite on brass the metal was permanently indented by the impinging 
sphere, so that consistent velocity curves could not be obtained. For 
these cases the mean charge is given for a range of velocities at which 
the charge was approximately constant. 

6. Discussion of Results. 
The results prove that intimate contact, without friction, between 
metals and dielectrics produces charges of the same order as those which 
were obtained by friction in the experiments previously mentioned. 
It is unlikely that any appreciable portion of the charge is due to friction. 
In both forms of the experiment, every precaution was taken to eliminate 
sliding contact of the surfaces. The lateral play of the ebonite disc was 
exceedingly small, and in the hurling experiments the sphere was pro- 
jected vertically so as to avoid slipping of the surfaces. The hurling cup 
fitted the sphere evenly, so that the ball could hardly have possessed 
any considerable rotation at the instant of collision, and the time of 
contact was probably only a minute fraction of a second, since the speed 
of separation due to the large values of the velocity and resiliency was 
further augmented by gravity. In all published accounts of electrifica- 
tion by friction, repeated mention is made of the erratic character of the 
effect, which extends even to the sign of the charge. In the present 
experiments there was never the slightest tendency towards a change of 
sign, and the value of the charge remained remarkably constant during 
any one set of runs extending over several days, although it varied 
between fairly wide limits during the course of several months. In the 



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302 HAROLD P. RICHARDS. [ISSSS 

entire work there were not more than ten instances when the metal 
received a negative charge, and all of these occurred immediately after 
the specimen had been cleaned with alcohol, making it clear that, in these 
cases, the surfaces had not dried completely. The charge was always 
positive even when it was produced by a contact of almost no velocity. 
Any residual friction would in all probability have been extremely 
variable in amount, and this variation, superimposed upon the erratic 
effect of constant friction, would have seriously affected the consistency 
of results. Upon several occasions the ebonite disc was rotated by hand 
upon the brass anvil, which acquired a charge sometimes positive and 
sometimes negative. Sliding friction may therefore be completely dis- 
missed in considering the results. 

Apparently electrification by impact is a surface effect. Since the area 
of surfaces actually in contact increases with velocity of impact, greater 
charges can be expected for the higher velocities. This would explain 
the velocity curves obtained. The secular variation in the amount of 
charge may be accounted for by the fact that alteration in the shape of 
the surfaces occurs during lapse of time and repeated collisions. 

It does not appear that there is any direct relation between the charge 
produced and the energy lost by collision. If Q and C represent, respec- 
tively, the charge and the capacity of the metallic system, and E the 
corresponding electrical energy, we may write Q = V2CE. If any 
constant fraction of the mechanical energy lost in impact at a given 
velocity were transformed into electrical energy, then E would be a 
constant for impact at that velocity, and the charge would vary directly 
as the square root of the capacity. Inasmuch as it has been shown that 
the charge is independent of the capacity, we may conclude that there 
is no direct dependence of the electrical energy upon the mechanical 
work performed in collision. As it seems probable that the frictional 
and impact effects are produced by the same mechanism, it is advisable 
to discuss the soundness of Jones's^ conclusions. He states that the 
charge produced by a given amount of frictional work increases with the 
capacity of the metallic system. However, he does not mention the 
values of the capacities used, giving one dimension only for the cylinders 
employed to vary the capacity. This dimension he terms variously the 
length or the ** thickness." Furthermore, his results are vitiated by a 
large secular variation, inasmuch as he found it necessary to perform 
complete runs at each of the different capacities in succession, whereas 
in the present experiments many readings could be taken alternately 
at the various capacities in a short time, so that not only would the 

> Loc. cit. 



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Na'4^^^*] ELECTRIFICATION BY IMPACT. 303 

secular change be small, but it could be eliminated by taking an average 
value. In this connection it may be noted that the recent work of 
McClelland and Power^ contradicts Jones's conclusions that the maximum 
charge is independent of the temperature and velocity of the rubbing 
surfaces. 

Further evidence in support of the view that there is no direct relation 
between the mechanical energy and the charge produced is furnished by 
the curves in Fig. 3. If, for a given velocity of impact, there were a direct 
proportionality between the electrical and mechanical energies, then in 
the expression given above, Q .= ^liCE, E would vary directly as the 
mass of the plunging system. Thus a reduction of 28 per cent, in the 
charge might be expected when the mass is reduced by 48 per cent. 
The actual decrease in the charge, however, was only 16 per cent. Addi- 
tional evidence is afforded by the wide variation in mechanical energy 
lost per unit charge. For the ebonite ball, using the mean charge 
(Fig. 6) produced at a velocity of 295 cm./sec, the coefficient of resiliency 
being 0.74, we find 1.76 X 10' ergs lost per e.s.u. of charge. A similar 
calculation for the ebonite disc (Fig. 2) gives 1.50 X lo* ergs per e.s.u. 
Owen^ finds that for ebonite rubbed with copper the same ratio has values 
ranging between 4.3 X lo* and 186.0 X lo*. 

So far as conservation of energy is concerned, the total electrical 
energy acquired is compensated by the mechanical work done in separat- 
ing the charged surfaces. This is apparent at once from the consideration 
that at the moment the charge is produced the layers of positive and 
negative electricity almost coincide and therefore the potential of the 
system is not appreciably raised. No deflection of the goldleaf occurs 
until the surfaces are separated. However, the failure of the charge to 
increase when additional pressure is added, unaccompanied by a sudden 
impact, indicates that a certain amount of work is required to effect the 
passage of electrons from the metal to the dielectric, although it is possible 
that static pressures much greater than those used in the present experi- 
ments would increase the electrification. In this connection it should 
be recalled that, in the photoelectric effect, work is done by the electrons 
in emerging from the surface film. But in the present case so small a 
portion of the energy lost in impact is utilized in this manner that it 
cannot be stated how much work is necessary to produce the charge. 
Probably in the case of two optically flat surfaces the velocity of impact 
necessary to produce a given charge would be much smaller than in the 
present experiments. 

1 Loc. cit. 
« Loc. cit. 



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304 HAROLD F. RICHARDS. ^SiS 

The results for repeated impacts with the ebonite disc (Fig. 4) show 
a limiting charge of 9.78 e.s.u. Some view such as that of Helmholtz, 
who regarded the frictional effect as similar to the contact difference of 
potential between metals, must be assumed to account for the direction 
of the effect. From this point of view a very high maximum potential 
of the metal might be expected, on account of the vastly greater concen- 
tration of free electrons in metals than in dielectrics. This is borne out 
by the experiments in which an ebonite disc impinged upon metal surfaces 
at various potentials (Table III.)» the charge produced showing no tend- 
ency towards a maximum. We may conclude, therefore, that the maxi- 
mum is conditioned rather by the amount of charge present upon the 
dielectric than by the potential of the metal anvil. 

In the experiment of repeated impacts with the ebonite ball, the latter 
was discharged between collisions. The curve (Fig. 4) shows that in 
this case there seems to be a tendency for the positive charge on the 
metal to leak back to the dielectric. This is at variance with the results 
mentioned in the preceding paragraph. This tendency towards back- 
leakage, however, might be greater for the sphere than for the disc, on 
account of the greater intimacy which higher velocities and curvature of 
surface would cause. The dissipation of energy per unit area is probably 
greater in the case of the sphere than of the disc, and the heat developed 
might also facilitate back-leakage. 

It is a pleasure to acknowledge here many valuable suggestions received 

from Professor L. T. More and Professor R. C. Gowdy during the course 

of the experiments. 

University of Cincinnati. 
February 11, 1920. 



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No"^^*] PRECISION X-RAY SPECTROMETER, 305 



A NEW DESIGN OF PRECISION X-RAY SPECTROMETER. 

By C. D. Cooksby. 

Synopsis. 

Principle of the Spectrometer. — The spectrometer is especially designed to make 
use of the ** Method of Displacement " already published, for the determination of 
X-ray wave-lengths. This method is briefly described. 

Description of the Spectrometer. — ^A detailed description of the spectrometer with 
a plan and side elevation are given. 

• Adjustments. — The processes involved in the adjustment of the spectrometer for 
precision measurements on X-ray wave-lengths are explained in detail. 

Verification of the Fundamental Assumption on which the ** Method of Displace- 
ment" is Based. — The method requires that a portion of the length of a beam of 
X-rays, after reflection, shall be of constant width. The possibility of this has 
been previously demonstrated on theoretical grounds. An exploration of the 
reflected beam for the ai line of the K series of silver has been made and the results 
are found to agree with theory. 

Principle. 

A METHOD has been devised for measuring wave-lengths in the 
X-ray region of the spectrum, by Professor H. S. Uhler,* which 
promises to eliminate many of the errors involved in earlier methods. 
The method requires the use of two slits of equal width between the 
source of rays and the crystal and a means of displacing the photographic 
plate in a straight line parallel to the line of coUimation of the spec- 
trometer, the plate undergoing no rotation during the displacement. 
The glancing angle of reflection at the crystal is then determined solely 
by the distance apart of the spectral lines, taken on both sides of the 
direct image of the slits in the two positions of the plate, and the distance 
through which the plate has been displaced. These distances can both 
be measured on the same comparator, thus making the determination 
of glancing angles depend solely on two linear measurements in the 
same units. 

This method of displacement for determining glancing angles was 
given a preliminary trial by Uhler and myselP in our work on the K 
series of gallium. The spectrometer we then used had not been con- 
structed originally for this method, but the results obtained with the 
remodelled apparatus encouraged us to believe that with a properly 
designed instrument the method would be capable of great precision. 

» Uhler. Phys. Rev., N.S., Vol. XI.. No. i. p. i, 1918. 

* Uhler and Cooksey, Phys. Rev., N.S., Vol. X., No. 6. p. 645, 1917. 



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3o6 



C. D. COOKSEY. 



rSBCOMD 

LSitMfiri. 



Description. 
The spectrometer is shown in plan and elevation in Figs, i and 2. 
The main part of the spectrometer consists of a heavy cast iron base A, 
in the form of a rectangle, about 78 cm. long by 29 cm. wide. At the 
center of one end of this base is a vertical bracket carrying a vertical 
slit, 5i, with adjustable gold jaws 2.4 mm. thick. The base A is pro- 
vided on one side with a V rail and on the other with a plane surface 
running parallel to the long axis of the rectangle. Another rectangular 
base, L, having a foot with a V groove at each end of one side, and a 
foot with a plane bottom at the middle of the other side, can slide on 
the rails of base A toward or away from Su A Soci6t6 Genevoise circular 
dividing engine, without its knife carriage, is bolted on the upper surface 
of L in such a manner that the axis of rotation of the revolving table 
is parallel to the long axis of Si. The normal from the center of Si to 
the axis of rotation forms the coUimating line of the spectrometer. A 
second slit, 52, similar to 5i, is fastened to the base of the dividing engine 




between its axis of rotation and 5i, and at the same height as 5i. St is 
normally at a distance of 4.5 cm. from the axis of rotation, but this 
distance can be altered by a few centimeters. 52 is provided with a 
slow motion adjustment by which it can be moved horizontally at right 
angles to the line of collimation. Another adjustment permits its rotation 
about this line or a parallel line as axis. 

The face-plate of the dividing engine has fastened at its center a 
brass plate with three V grooves 120° apart, radiating from the axis of 
rotation. Two stands, not shown in the figures, are provided with three 
legs each to fit into these grooves. One of these stands has fastened to 
it the crystal holder. This holder has two horizontal linear adjustments, 
one parallel to, and the other at right angles to, the crystal face. A third 



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Vol. XVI.I 
No. 4. J 



PRECISION X-RAY SPECTROMETER, 



307 



adjustment permits the crystal to be rotated about a horizontal axis 
parallel to its face. The other stand supports a slit, 58, used only in 
adjusting the spectrometer. This slit is of fixed width of about 0.02 
mm., and the jaws of the slit, when in place, do not come above the 
coUimating line. Thus this slit does not limit those rays coming through 
5i and St which are directed above the collimating line when they reach 
the third slit. 58 is provided with adjustments by which the center of 
the upper end of the opening between the jaws can be made to remain 
accurately in the axis of rotation while the divided circle is turned through 
360*^. This adjustment was made under a high-power microscope, pro- 
vided with cross hairs, and the fact that it is possible to so adjust the 
slit that no motion of the point referred to can be detected when the 
divided circle is rotated shows that the axle and bearings of the dividing 
engine are very true. 

On the dividing engine base, diametrically opposite St is mounted a 
pair of rails, D, about 42 cm. long and 10 cm. between centers. The 
casting carrying these rails is pivoted on the engine base so that the rails 
can be made parallel to the line of collimation. One of these rails is 



I rr 



I 



^ 



f*tite--|f— - 




Fig. 2. 

V-shaped in section, and the other square, with its upper surface plane. 
They were very carefully machined and ground smooth. 

A carriage, K, fits on these rails and is furnished with a clamping screw 
to lock it tight to them at any point of their length. The extreme dis- 
tance of this carriage from the axis of rotation of the spectrometer can 
be limited by an adjustable stop clamped to one of the rails, or by a rod 
of known length placed between the stop and the end of the carriage. 
It is this feature which permits the use of the *' Method of Displacement" 



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308 C. D. COOKSEY. ' [^^ 

already referred to. The end of the carriage nearer St has fastened to it 
a horizontal aluminium rail, E, 42 cm. long, with its long axis at right 
angles to the direction of motion of the carriage. The transverse section 
of this rail is an inverted T. A horizontal brass semicircle, F, with a 
flange projecting vertically downward can be clamped on the T rail at 
any point. A flat brass plate, G, rests on top of the semicircle and is 
pivoted at its center. It can be rotated on the semicircle and clamped 
at any desired angle, F and G together forming a sort of protractor. 

The plateholder, if, is a cast aluminium rectangular box, with plane 
surfaces inside, against which the plate can be pressed flat by means of 
strong springs on a wooden cover at the back. To allow for variations 
in the thickness of plates, the cover is lined with thick felt on the inside. 
A rectangular opening about 24 cm. long by 1.5 cm. high is cut in the 
front of the box and covei'ed with black paper. The paper can easily 
be removed to permit a view through the plateholder or the measurement 
of the distance from the plate to the axis of rotation. The plateholder 
accommodates plates 25.4 cm. by 3 cm., the latter figure being determined 
by the dimensions of the device for holding the plates on the comparator 
used for measuring them. The central portion of the bottom of the 
casting extends behind the plane of the back of the rectangle in the form 
of a tongue, the bottom of which was machined flat. This tongue is 
provided with two dowel pins and a screw by which the plateholder can 
be screwed tight to the azimuth plate, G. 

Adjustments. 

The object of this method of mounting the plateholder is to be able 
to photograph several spectral lines at a long distance from the direct 
beam without having to use excessively long plates and to be able to 
adjust the plane of the plate so that it may be either at right angles to 
the collimating line, or to the beam reflected from the crystal. A very 
convenient use of the aluminium T rail is in taking what I call "Range 
Plates." In using two very narrow slits it is necessary to know very 
closely what setting of the crystal gives the best reflection for a particular 
wave-length. To ascertain this a series of exposures of equal length are 
taken on the same plate, the plateholder being displaced a small distance 
along the T rail between each exposure, and the crystal setting altered 
a small amount. A comparison of these exposures shows, not only the 
best setting of the crystal, but, if enough are taken, the effective range 
of reflection of the crystal for the particular width of slits chosen. 

The object of mounting the plateholder, crystal, and 52 on a separate 
base from that on which 5i is mounted is to be able to conveniently 



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Na'4?^^^'] PRECISION X^RAY SPECTROMETER. 309 

vary the distance between Si and the axis of rotation of the spectrometer, 
which at the same time would, of course, vary the distance between Si 
and Si, The distance of Si from the axis can be varied from about 11 
cm. to about 35 cm. 

The base A of the spectrometer is pivoted on a triangular cast iron 
base, B, in such a manner that A can be given a small rotation about the 
long axis of Si as axis. The base B rests, in turn, on a similar base, C, 
provided with ways on which B can slide a short distance at right angles 
to the collimating line. The base C is supported on leveling screws. 
Finally the table of the spectrometer can be rotated back and forth 
through a small angle by means of a spring motor connected to the 
tangent screw of the dividing engine through a connecting rod and crank. 

The object of this rather elaborate mounting is to facilitate the lining 
up of the spectrometer with the focal spot on the anti-cathode of the 
X-ray tube. In working with soft X-rays it is necessary to have a 
window in the tube which will not absorb too much of the energy. Thin 
aluminium is very good for this purpose, but, when very thin, the window 
must be quite small, thus giving an emergent pencil of rays of small 
angular width. Experience has taught me that it is quite difficult, 
without special means, to make the collimating axis of the spectrometer 
coincide with the axis of this pencil. This adjustment is simple with 
the mounting described above. The instrument is first brought roughly 
into line with the aid of a fluorescent screen. A plate is then placed 
immediately behind Si and two exposures taken on it; a long exposure 
with the slit narrow and a short one with the slit wide open or removed 
entirely. This gives the projected images of the slit and the aluminium 
window superposed on each other. The center of the image of the 
window is then marked with a fine scratch, and the plate replaced in 
the position in which it was when the exposures were taken. By focusing 
the cross hairs of a microscope on the center of the image of the window, 
and moving the spectrometer across base C till the image of the slit 
comes under the cross hairs, Si is brought into the axis of the pencil of 
X-rays. In order to bring the collimating line of the spectrometer in 
coincidence with the axis of the pencil, 58 is placed in position on the 
spectrometer table, and a plate placed immediately behind it. An expo- 
sure is then taken with Si narrow, and, if the lineup is badly out, another 
with Si wide open, and a screen placed directly above 58. This gives 
two images, one above the other; the center of the upper one gives the 
position of the axis of the pencil, while the center of the lower one gives 
the position of the axis of rotation of the spectrometer with respect to 
the former. The plate is replaced on the spectrometer, and a microscope 



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3IO C. D. COOKSEY. gj^ 

focused on the center of the upper image. The spectrometer is then 
rotated on base B, about Si as an axis, till the image of 5s comes under 
the cross hairs. The axis of the pencil of rays coming through the 
window on the tube will then pass through Si and the axis of rotation 
of the spectrometer. This being done, a similar method of superposed 
exposures will show the position of St with respect to the coUimating 
line, and any error can be corrected by means of the transverse adjust- 
ment referred to above. By means of a pair of parallels temporarily 
supported on the divided circle and extending between Si and 5i, the 
plateholder can be placed first in front of one slit, and then in front of 
the other without any rotation about the normal to the plate. Images 
of both slits can be taken close together on the same plate and any lack 
of parallelism between the slits corrected by means of the rotational 
adjustment on St referred to above. 

The rails D are made parallel to the collimating line by making Si 
and St very narrow, and taking one exposure on the upper half of the 
plate when it is directly over the bearing on which the rails are pivoted, 
and a second on the lower half of the plate when it is at the extreme 
end of the rails. The rails can then be rotated so that their extreme 
end moves through the distance between these images. The straightness 
of the rails was tested by covering the plate with a screen having a 
narrow horizontal slit, and taking exposures with Si and 5s narrow and 
the plate at different positions on the rails, the horizontal slit being 
moved vertically by its own width between each exposure. At the time 
of writing, the rails have been found to be very true, though there seems 
to be a very slight transverse shift of the plate when moved between 
certain positions. This may be due to dirt, but if it persists in future 
tests it can easily be measured and allowed for in determining wave- 
lengths by the '* Method of Displacement." 

The azimuth angle between the normal to the plane of the plate and 
the collimating line is completely determined by the difference in distance 
between the same spectral line photographed on each side of the central 
beam in two different positions of the plate on the rails P, and the distance 
between these positions. This angle can be made zero by rotating the 
plate G on the circle F or can be applied as a correction in the calculation 
of wave-lengths. 

If the plane of the crystal is not exactly parallel to the axis of rotation 
of the spectrometer, the lines taken on either side of the central beam 
will be inclined to each other by four times the angle between the plane 
of the crystal and the axis. If two plates are taken at the same distance 
from the axis of rotation, each with the same line on both sides of the 



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Na'4^^''] PRECISION X-RAY SPECTROMETER, 3II 

central beam, and are then placed with their gelatin sides together, and 
the top of one at the bottom of the other, in such a manner that the 
corresponding lines on one side of the center are superposed, then the 
corresponding lines on the other side will be inclined to each other by 
eight times the angle of tilt of the crystal. This makes a very delicate 
method of detecting any error in the adjustment of the crystal face. 

Verification of the Theory. 

It has been shown theoretically by Uhler^ that a certain portion of a 
beam of monochromatic X-rays passing through two slits of equal width 
and reflected from a crystal is of a rectangular cross-section in a plane 
normal to the mutually parallel long axes of the slits, the length of the 
rectangular portion being equal to the distance between the slits, and 
the width being equal to the width of the slits. I have explored this 
rectangular portion of the beam in the case of the ai line of the K series 
of silver. The distances from the axis of rotation to Si and St were 20 
cm. and 4.5 cm. respectively, thus making the rectangular portion of 
the reflected beam 15.5 cm. long. Exposures were taken on the same 
plate at both ends of the rectangle and at points one quarter, one half, 
and three quarters of its length. This was done with both slits about 
0.02 mm. wide and again with them o.i mm. wide. During the exposures 
the crystal was rotated back and forth through an angle of 3' about the 
position which gave the best reflection. 

The results of these photographs are in good agreement with Uhler's 
deduction that the portion of the reflected beam between the foci of the 
slits is rectangular in cross-section and of the same width as the slits. 
The exposures with the wider slits were purposely made short that 
they might bring out any lack of uniformity in the distribution of energy 
across the width of the beam at the different parts of its length. The 
results showed that the energy was fairly uniformly distributed and that, 
if the lines were thoroughly exposed, there should be no danger of an 
asymmetric blackening with respect to their axes. 

Though this spectrometer has not yet been used for the direct deter- 
mination of wave-lengths, every indication points to its giving a high 
degree of precision in such work. It should be pointed out here that 
there is nothing about the construction of the instrument to prevent 
its being used in the ordinary way for determining glancing angles by 
measuring the distance of the plate from the axis of rotation. Indeed, 
a determination of the glancing angle by both methods might give a 
measure of the depth of the mean reflecting plane of the crystal. 

1 Loc. ciL 



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312 CD. COOKSEY. 

In conclusion I wish to express my thanks to Professor Uhler for his 

many helpful suggestions and advice in connection with the design and 

adjusting of this instrument and especially for the plateholder and its 

adjustable mounting which were designed by him. 

Sloans I'htsxcal Laboratory, 
Yale Uniyerstty. 
March 15, 1920. 



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Na'4?^^*] ^^^ PERFORMANCE OF CONICAL HORNS. 313 



THE PERFORMANCE OF CONICAL HORNS. 

By G. W. Stewart. 

Synopsis. 

The experiments were performed to secure quantitative results with a conical 
horn used as a receiver. The approximate theory of A. G. Webster, when extended, 
and the experimental data herein presented lead to the following conclusions con- 
cerning such a horn acting as a receiver: 

IntensUy at Vertex as a Function of Frequency. — The experimental vaiiations of 
intensity at the vertex plotted with changing frequency, intensity of the arriving 
waves constant, demonstrate that: 

(a) The frequencies producing resonance are very closely integral multiples of 
the fundamental frequency. 

(b) The resonance peaks broaden and the minima between the peaks increase 
with increasing frequency. 

(c) Therefore the conical horn used as a receiver gives an amplification for any 
frequency nearly the same or greater than the fundamental. 

(d) The greater the trequency, the less the differences between maxima and 
minima, and thus a horn long compared to the wave-length of the least frequency 
involved, gives an amplification without highly marked resonance characteristics. 

(e) The function of frequency obtained experimentally varies with the horn 
angle chosen, but retains the same general character. 

Optimum Horn Angle for Fundamental Resonance. — There is a horn angle for 
which the amplification will be a maximum, assuming fundamental resonance. 
The optimum angle is greater the higher the frequency, 256 and 512 d.v. being used. 

Optimum Hdm Angle; Overtones. — Using 512 d.v. as the fundamental and first 
and second overtone, similarly 256 d.v. as the fundamental and first overtone, the 
optimum horn angle decreases with the order of the harmonic, being greatest for 
the fundamental. 

End Correction. — The end correction of the conical horn is approximately 0.7 
of the radius. 

Conical Attachments. — Cylindrical and conical attachments to a conical horn intro- 
duce their own resonance characteristics, which may be estimated as to frequency by 
treating the end attached as a free open end but applying a positive correction to 
the length if the angle of the attached tube is less, and a negative correction if greater. 

Limitations of Conclusions. — The conclusions apply strictly to the limits of 
frequency used in the experiment. Nevertheless they make more clear the nature 
of the action for all frequencies. 

THE published theory^ of the action of conical horns and pipes is 
unsatisfactory in at least two respects, namely, there is a masking 
of certain physical aspects of the action through the assumption of 
spherical waves, and there exists too great an inaccuracy in these com- 

» See Rayleigh's Theory of Sound, Vol. II., Ch. XIV., and Barton, Phil. Mag.. Series 5, 
Vol. 15, 1908, pp. 69-81. and Webster, Proc. Nat'l. Acad, of Sciences, Vol. 5, p. 275, 1919. 



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314 O. W. STEWART. [ISS 

puted quantitative relations which should enable one to antitipate the 
amplification produced by a conical horn when used as a receiver. The 
present contribution furnishes certain quantitative information concern- 
ing the action of conical horns as receivers, under conditions as specified, 
and also givps a brief explanatory discussion expressed in terms of the 
physical action involved. 

I. Apparatus and Methods. 

Sources of Sound, — ^The sources of sound were two electrically driven 
tuning forks mounted upon wooden box resonators having openings of 
10 X 5 cm. for the 256 fork and 7.3 x 3.7 cm. for the 512 fork. 

General Method of Measurement. — ^A Rayleigh disc, connected by 
rubber tubing to the conical horn investigated, was used to obtain the 
relative intensities of the sound in the conical horn. The internal 
diameter of the rubber tubing was .45 cm. and the length about 150 cm. 
Readings were taken by the means of a telescope and scale. The 
deflections of the disc were proportional to the intensities in the disc and 
hence to the intensities at the vertices of the horns. A disc was con- 
structed for each frequency, the upper one shown in Fig. i being for 
the 512 fork. 

Location. — ^The source of sound, horn and disc were mounted on the 
edge of the roof of the physical laboratory 21 meters high, where the 



JL 



30 cm 



44.4 cm 



Fig. 1. 



absence of other buildings, combined with the elevation of the site, made 
the reflection of sound nil, excepting that from the root itself. This 
reflection was diminished in two ways: first, by covering the adjacent 
portions of the roof with thick hair felt whose absorption coefficient is 
about 50 per cent, and by mounting the fork and horn approximately 
150 cm. above the roof and separating them from each other not further 
than this same distance. Thus the effect of roof reflection was reduced 
to a small per cent. However, the proximity of the horn and fork 



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NaV^^^*] ^^^ PERFORMANCE OF CONICAL HORNS, 315 

introduced an error in that the wave falling upon the horn was not 
strictly plane, though in all cases the wave surface deviated from a plane 
only by a small fraction of a wave-length. 

Horns. — ^The horns were made of galvanized iron, U. S. standard 
plate No. 24. It' was found that, if thin metal were used, there was 
resonance in the conical wall affording sufficient dissipation to affect the 
intensity in the horn itself. This effect could be demonstrated by chang- 
ing the rigidity of the clamping of the horn. With the horns actually 
used, however, the intensity measurement was not capable of being 
changed by clamping and the walls did not vibrate noticeably. Inas- 
much as the absorption of the metal when not vibrating is very small, 
it is assumed that the results here presented are those found in conical 
horns having rigid walls and possessing no absorption. 

Each horn was cut off at the vertex, leaving a diameter of 0.5 cm.; 
thick wall rubber tubing 0.45 cm. in internal diameter and approximately 
150 cm. in length, was slipped over the open vertex and connected to 
the Rayleigh disc. 

In many of the experiments the lengths of the horns were altered a 
few centimeters in order to produce the length required for resonance. 
This was accomplished by means of heavy drawing paper slipped over 
the large end. It was experimentally shown that when the length of 
the addition of drawing paper did not exceed a few centimeters the paper 
served just as well as metal itself. The reason is, of course, that the 
changes in pressure near the large end of the horn are small. 

Detailed Method, — Deflections of the disc were read and assumed (and 
justifiably so) to be proportional to the intensities in the horns. But 
in order that measurements of relative intensities with varying experi- 
mental conditions might be secured, corrections were made for the lack 
of constancy in the intensity of the source of sound, and for the change 
of sensitiveness of the disc caused by changes of temperature. The data 
for the first correction were obtained by microscopic measurement of 
the amplitude of the fork at the time of each reading of the disc. The 
second correction was secured through an occasional reading of the disc 
when attached to a tube terminating in a position fixed relative to the 
source of sound, the amplitude of the fork being noted. The details of 
applying these corrections are simple and almost obvious. The only 
assumption involved is that the intensity is proportional to the square 
of the amplitude of the fork. 



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3^6 



G. W, STEWART. 



Sbcomo 



II. Experimental Results. 
The experimental results herein presented are not as accurate as can 
be obtained, but they will give fairly satisfactory quantitative information 
concerning the action of conical horns. The experimental conditions 




Fig. 2. 

necessary to obtain more accurate results are difficult to secure. The 
experimental points shown in the curves are usually each the result of 
a single setting and observation. Nevertheless, they do not comprise 
the entire data but are merely typical. All results have been corrected 
for temperature, the reduction being made to 20*^ C. 




Fig. 3. 

Variation of Intensity with Length, Frequency Constant, — ^The first 
question one might ask in regard to the action of a conical horn or tube 
acting as a receiver is in regard to the resonance characteristics and the 



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Vol. XVI.l 
No. 4. tJ 



THE PERFORMANCE OP CONICAL HORNS. 



317 



•amplifying eflFect throughout the range of frequencies of interest. A 
series of trials was made with conical horns of constant angle but of 
varying length, using the same source of sound. The data were taken 
on several evenings and are shown, after corrections are made for the 



Zo^ 




^ /i 



> 



luno J'V 



V.v 



Fig. 4. 



7?/ 



effect of temperature di£Ferences upon length, in the full line curve plotted 
in Fig. 2. Over two portions of the curve magnifications of 40 and 20 
are also plotted. There should be added to the data in Fig. 2 an im- 
portant relevant fact, namely, that the intensity without the horn as 
tested by an open tube at the position occupied by the open end of the 




Fig. 5. 

horn, was of the same order as the observation with the horn of shortest 
length. 

Variation of Intensity with Angle in a Conical Horn, Assuming Maxi- 
mum Resonance and Fundamental Frequency. — In Fig. 3 it is shown that 



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318 



G. W. STEWART. 



rSacoND 
LSniBS. 



the maximum intensity at resonance occurs when the ratio of radial 
length to diameter of opening is approximately 5 : i for a frequency of 
256 d.v. 

Fig. 4 gives similar information in regard to the frequency of 512 d.v. 
Here the optimum ratio is approximately 4:1, that is, the radial length 
if four times the diameter of the open end. The observations indicated 




Fig. 6. 



by circles and crosses were taken at other times. There appears a dis- 
agreement of peak location for the 4 : i probably due to an error in 
reading of i cm. 

Resonance Peaks, Similar to those in Figs. 3 and 4, but with a Frequency 
of the First Overtone. — Fig. 5 for 256 d.v. and Fig. 6 for 512 d.v. are self- 
explanatory. Again crosses and dots in- 
dicate separate series. The point worthy 
of note is that, frequency constant, the 
optimum angle decreases when the horn 
is lengthened so that the fundamental 
becomes the first overtone. 

Resonance Peaks, with Frequency that 
of the Second Overtone. — ^With 512 d.v. 
only observations on two horns were 
taken and these are shown in Fig. 7. 
Although these data are too meager to 
interpret accurately, yet there is sufficient evidence that the optimum 
angle continues to decrease with an increase in the order of the overtone. 
Variation in Optimum Angle with Order of Overtone. — Fig. 8 shows how 
the optimum angle changes with the order of the overtone and it is here 
seen that the/atio of change for the 256 and 512 is approximately the 
same. The reliability of the data gives only a general idea of the change. 




Length Iti lie 
Ratio C: I 



Fig. 7. 



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Vol. XVLl 
No. 4. J 



THE PERFORMANCE OP CONICAL HORNS. 



319 



Effect upon Resonance Characteristics of Conical and Cylindrical Attach- 
ments. — It is to be anticipated that the resonance characteristics of the 
tube attached to a conical horn for listening purposes will be super- 
imposed upon the characteristics of the cone itself. By simple tests 
with a tonometer and attached cones and cylindrical tubes the writer 
found that the resonance frequencies of the attachments can be estimated 
by the following rule: The attached tube, cylindrical or conical, will 
introduce resonance characteristics which may be computed as to 




Fig. 8. 

frequency by treating the end attached as a free open end but at the same 
time remembering that if the angle of the attached tube is less than that 
of the conical horn there is a positive end correction and if greater a 
negative end correction. 

Directivity of a Conical Horn. — ^As is well known, when the source of 
sound is along the extended axis of the horn, the greatest intensity is 
produced at the vertex. This effect, because it depends upon the phase 
relations at the opening, becomes more marked the larger the opening 
of the horn. This comment is introduced merely because in practical 
application of the conical horn as a receiver, the exclusion of side noises 
is of great importance. 

End Correction. — ^The experiments may be used to determine, the end 
correction of a conical horn. If we assume that, 

L + KR--n-, 
2 

where L is the length of the horn, R the radius, K sl correction factor, and 
n an integer, and plot L/n, and R/n as coordinates, K may be computed 
from the slope. If the results are in agreement with the above linear 
relation, it may reasonably be concluded that the resonance frequencies 
are integral multiples of the fundamental. The results of the experi- 



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320 G. W. STEWART. ^5SS! 

ments have been so plotted and the assumption of the linear relation 
seems to be fully justified, whether the frequency is a fundamental or an 
overtone. The value of K appears to be 0.7, with a possible error of 10 
per cent. Experiments can readily be designed to determine the exact 
relation between the resonance frequencies of the conical horn, and thus 
the end correction, with a much greater accuracy than here employed. 

III. Theory. 
A brief reference to theory will aid in extending the application of the 
experimental results and in understanding the action of the conical horn. 
The only theory of which the writer is aware that offers a possibility of 
obtaining quantitative results for conical horns is that of Dr. A. G. 
Webster^ of Clark University. In this theory he makes the following 
assumptions: 

(a) That the tube or horn has a cross-section which is always small 
but is a function of the length, x. 

(b) That the sound waves travelling in positive and negative direc- 
tions of X are plane, i.e., all Variations in y and z directions are zero. 

(c) That the conductivity for an open end is the same as a channel of 
a selected length. 

(d) That the general equations of sound are applicable. 

It will be necessary to extend the published work of Webster somewhat 
in order that we may secure the quantitative results. Let X be the 
volume of air periodically entering the horn under a maximum excess 
pressure p, and z be the impedance and equal to p/x (see Webster, loc. 
cit.). Let subscripts 1,2, and 3 refer respectively to the values at the 
small end of the horn or in this case the vertex, the opening of the horn, 
and outside the opening at a point where the influence of the horn can 
be considered as vanishingly small. Assume the distance between pt 
and p9 to be small compared with a wave-length and that Zq represents 
the impedance of the opening treated as a short tube or channel, the air 
escaping from a circular hole in an infinite plane. Then, by definition, 

_ p2 — pi _ Z2X2 — pt _ pz 

Zq Zq Z\ — Zq 

But according to Webster, equation (24) 

X2 = cpx + iXx = {cZx + d)Xu 
where c and d are defined as follows: 

__ — <r^\ sin k(l + €1 — 62) , __ (TiX\ sin fe(/ — 62) 

j8jC2 sin kt\ sin kt% ' (T\X% 

» Loc. cit. 



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Na*4^'] ^^^ PERFORMANCE OP CONICAL HORNS. 32 I 

<ri and ai represent the cross sections at the small and large ends, respec- 
tively, fi = pa*k, where p is density, a velocity of sound, and k the 
frequency divided by the velocity, Xi and X2 represent the distances from 
the vertex of the small and large ends respectively, and 

I ^ Xi- Xu 

tan k€i = kxu 
tan k€i = kxi; 



But since 



with 



then 



• ^ ' Zi {cZi + d) {cZi + d) (Z, - Zo) 

aZi + b 
Zt = y , , (Webster's equation (25)), 

Xx s'n *(/ + €1) jS xi . _ _ 

a = : — r , 6 = sm W, 

Xt sin ie<i (Ti Xs 



. Zipi 

p\ = 



<-+«(^!-^-)' 



and we have a relation between the exterior and vertex maximum excess 
pressures; and these pressures are proportional to the square roots of 
the respective intensities. 

For the conical horn closed at the vertex, 

2l = «, 

and therefore 

. Pl__ 

^' ~ (a - cz^) • 

Now Webster shows that, assuming the conductivity of the open end 
to be that of a short tube of conductivity Co, ending in an infinite plane. 



So = (>a}k^ 



\2X Co/ 



Hence the complete expression that will enable us to determine quanti- 
tative relationship between the incident sound intensity and that found 
at the vertex is 

p p* 

Xi sin k{l + €1) ffjifexi sin k{l + ti — 



+ 



I \2ir Co / 



X2 sin k€i X2 sin kei sin k€2 

and if p is to be determined for the vertex, Xi = o, 

*^^ sin kx2 <T2 sin k(x2 "" ^2) /_^ . £_ V 

kX2 X2Sin*€2 \2v Co/ 



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322 C. W. STEWART, [^SS? 

It can be shown (Professor Webster has shown this, as well as the deriva- 
tion just given by the author, but has not published either) that Webster's 
theory may be modified by omitting the assiunption of small cross 
section, and by assuming spherical waves, p being a function of r, the 
radial length, and the time, with the following equation: 



infer (T sin { kr ~ 6) / ^ . i_ V 
kr rsinJfe€ \2ir CqJ 



where 

tan Jfe€ = Jfer. 

For our case of conical horns (2) is the more accurate. 

For the conductivity Cq, it is assumed that the open end is equivalent 
to a channel if length 0.6 of the radius, Thus 

^" " 0.6 X i? "" 0.6 • 

With this value of Co and using (2), computations were made and 
relative values of {pi/pzY or relative values of the intensity, were secured. 
In computing, one must of course use the modulus of the fraction in the 
above equation. The results are plotted in the dotted curve in Fig. 2. 

An additional point of the theory should be noted. Equation (2) 
indicates that the computed values depend upon the product kr which 
is proportional to the product of radial length and frequency. In Fig. 2, 
the experimental results were plotted with changing radial length, 
frequency remaining constant. From the foregoing statement it is 
obvious that precisely the same curve would have been obtained with 
varying frequency, radial length constant, the values of the ordinates 
depending only upon the product of radial length and frequency. 

IV. Discussion of Results. 

Extension of Results. Fig. 2. — Inasmuch as we are apparently justi- 
fied, by the preceding theoretical considerations, in regarding Fig. 2 as 
showing the relationship between relative intensity and frequency, the 
following conclusions may be stated : 

(a) The frequencies producing resonance are very closely integral 
multiples of the fundamental frequency. 

(6) The resonance peaks broaden with increasing frequency. 

(c) The intensity values for the minima, located between the resonance 
peaks, increase with increasing frequency. 

((f) The conical horn gives a very considerable amplification for any 
frequency nearly the same as or greater than the fundamental frequency. 



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No^4?^^'] ^^^ PERFORMANCE OP CONICAL HORNS. 323 

(The ordinate at the beginning of the curve is in fact no greater than the 
relative intensity without the horn at all.) 

{e) The greater the frequency, the less the difference between maxima 
and minima relative intensities, the curve promising to approach one of 
smaller and smaller undulations, yet one representing a great amplifica- 
tion. 

These conclusions indicate that if a horn, long compared to the wave- 
length of the least frequency involved, is used as a receiver, it promises 
amplification without highly marked resonance characteristics. Experi- 
mental tests of this conclusion have been made, and with satisfactory 
verification.^ 

Utilization of Results, — In the utilization of the results of the foregoing 
experimental and theoretical discussion it must be remembered that the 
existence of the optimum angle and its alteration with the order of the 
overtone, prevents the experimental curve in Fig. 2 from being regarded 
as quantitatively typical. In fact, if the horn ratio had been approxi- 
mately 7 : 1 instead of 5 : i, the second resonance peak would have been 
higher than the first. In general, since there exists an optimum angle, 
the relative values of the amplification at the various resonance fre- 
quencies must depend upon the angle of the horn. It would be advan- 
tageous to have information concerning the effect of various frequencies, 
with a variation of the ratio and length of the horn, for then one could 
ascertain just what effects any conical horn would have, acting as a 
receiver for any sound of known frequencies. It is believed that the 
present results furnish a partial guide in the design of a conical horn 
for any purpose, particularly by way of suggestion as to what trials 
should be made to secure the desired horn. 

Physical Aspects. — ^An explanation in physical terms will assist in 
understanding the causes for the characteristics of the curve in Fig. 2. 
Assume for the moment that the length of the conical horn is short 
compared with the wave-length, and that the horn opening is a part of 
a plane wall. The horn would thus reflect the sound with approximately 
the same effect as any other equal area of wall surface, or surfaces sup- 
posed to be perfect reflectors. We would then expect to find the horn 
acting as a reflector and not as a collector. This reflecting function of 
the conical horn persists irrespective of its dimensions, though of course 
as the length of horn becomes comparable to the wave-length of the sound, 
the reflection cannot be considered as in the same phase from the entire 
inner surface, but each element of area is a source of sound in such phase 
and amplitude that combined with the oncoming sound will result in a 

» Stewart, Phys. Rev.. XIV.. a. 1919, p. 166. 



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324 G. W. STEWART, ^^^ 

zero value of the velocity potential over the wall surface. In the conical 
horn, then, reflection takes place throughout its entire length, this 
reflection being in all directions away from the inner surface just as if 
each element of that surface is a source of sound. 

It is a consideration of this reflection which makes clear the reason for 
the lack of concentrating ability shown in that part of Fig. 2 to the left 
of the first resonance peak. Even when the radial length of the horn 
is approximately one-half of that for maximum resonance, the intensifica- 
tion produced by the horn is almost unnoticeable. In other words, the 
horn acts much like a plane reflector that subtends the same angle at the 
source and the energy is approximately the same at the vertex as if the 
opening were a hole in that plane. 

Just as there is reflection from the walls of the incoming wave, so 
also there is reflection of the outgoing wave. In this latter reflection 
from the walls we find an explanation of the fact that the minima in 
Fig. 2 are not constant, showing zero amplification. Conditions for 
resonance demand reflection* not only at a distant end but also at the 
opening where the incoming wave enters. In the conical tube, inasmuch 
as we have reflection of the outgoing wave throughout the entire length 
of the wall, there is always a certain amount of reflection at the point 
where the phase of the incoming wave and the just reflected portion of 
the outgoing wave are the same. There would thus be *' resonance." 
According to this explanation there should be resonance for any frequency 
greater than the fundamental, for with every such frequency there is in 
at least one region of the inner surface a reflection of the outgoing wave 
with the above stated phase relations, thus furnishing the necessary 
conditions for resonance. Fig. 2 is in agreement with this conclusion 
in that the minima show a distinct amplification. As an illustration 
of the above explanation, suppose the horn has a length corresponding 
to the first minimum of Fig. 2. The reflection from the opening of the 
outgoing wave is opposite (approximately) in phase to the incoming 
wave. In a cylindrical tube this would be the cause of zero amplification. 
But in the conical horn there is reflection from the wall near the opening 
which, being reflection without change of phase, will be in phase (approxi- 
mately) with the incoming wave. Resonance will therefore exist. 

In this connection the writer wishes to emphasize that the usual view 
of the conical horn, i.e., that it acts primarily as a concentrator, is mis- 
leading, and that the view of it as a resonator will, in most applications 
be much more satisfactory and helpful. Of course, both concentration 
and resonance are present and which predominates depends upon the 
dimensions of the horn and of the length of the wave. 



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Na*4?^^'l ^^^ PERFORMANCE OP CONICAL HORNS. 325 

In the usual theory, giving the resonating frequencies in conical tubes,^ 
it is assumed that the incoming and outgoing waves are spherical within 
the tube and the results derived for the natural frequencies are approxi- 
mately correct. But the assumption of sphericity is in effect an assump- 
tion of reflection from the walls throughout the length for otherwise there 
C9uld not exist these imagined portions of spherical waves. In a portion 
of Webster's theory, to which reference has been made, plane waves 
are assumed in the case of a tube whose cross-section is always small, 
and spherical waves in the tubes not so limited, but there are applied 
hydrodynamic equations which permit reflections to exist. In the as- 
sumption of an approximately plane wave or a spherical wave reflections 
are virtually assumed, for these are necessary to maintain the stated 
shape of the wave. Thus it will be seen that existing theroies of the 
action of conical horns give approximate results for the natural frequencies 
because they distinctly assume reflection throughout the length of the 
walls, though without specific mention. 

There are further points which should be considered from a phe- 
nomenon viewpoint, especially since our theory gives us no direct 
assistance toward an explanation. Two of these are the reasons for an 
optimum angle and the variation of the optimum with frequency and 
with the order of overtone. It is believed by the writer that the existence 
of the optimum angle is occasioned by the fact that the horn has a diam- 
eter not vanishingly small as compared with a wave-length and hence 
the vibrations are not merely radial. Obviously then, certain angles 
would be expected to give the optimum resonance. A theoretical in- 
vestigation of these nonradial vibrations is now being made and a further 
discussion of the optimunl angle will be postponed. 

Errors. — ^The experimental results exhibited in this report should be 
interpreted in the light of the conditions under which they were under- 
taken. The results are and must be inaccurate because the conditions 
that would make possible accurate measurements cannot be had. In 
these experiments the horn is really a frustrum of a cone with a flux of 
energy through the "listening" tube attached at the several vertices. 
Inasmuch as the effect of the tube upon the intensity at the point of 
attachment in any case depends upon the area, length, damping, and 
resonance characteristics of the tube, it is not possible to establish 
experimentally a universally applicable statement of variation of rela- 
tive intensification of the sound as dependent upon the length and angle 
of the horn and frequency of the sound used. It is to be observed, how- 
ever, that, with the area and the length of the rubber tubing used in these 

* See Rayleigh and also Barton, loc. cit. 



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326 C. W. STEWART. . [^£? 

experiments, the flux of energy would seem not to be great enough to 
destroy the value of the relative intensities obtained regarded as an 
approximation to the truth, that the damping in the tubing was suffi- 
ciently great to make the resonance in itself very small indeed, and that, 
in fact, inasmuch as the length of the tubing was kept constant and 
different frequencies are not compared, the small resonance effect which 
might exist did not seriously modify the variation of relative intensity 
with the angle and length of the horn. It is believed by the writer that, 
when all the physical conditions are given appropriate consideration, 
one is justified in accepting the results herein described as furnishing a 
fair idea of the relative intensities at the vertices of conical horns. 

In conclusion, I wish to acknowledge the valuable assistance of Mr. 
Eugene M. Berry. 

Physical Laboratory, 

State University op Iowa. 



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No%^] ^'^^ FREQUENCY SPECTRA OP LEAD ISOTOPES, 327 



THE HIGH FREQUENCY SPECTRA OF LEAD ISOTOPES. 
By C. D. Cooksby and D. Cooksby. 

Synopsis. 

Least DetecUMe Difference in Wave4eng^h Dependent on Distance between Lines 
and Length of Reflected Ray. — Reasons are given for confining the work to a com- 
parison of the Lai lines of ordinary and uranio-lead. The least detectable difference 
in wave-length between two lines on the same plate is directly proportional to the 
least detectable distance between their axes and inversely to the length of the 
reflected ray between the crystal and plate. However, the nature of the Lai line of 
lead is such as to make it more important to reduce as much as possible the least 
detectable distance between the lines, than it is to increase the length of the reflected 
ray. 

LimU of Accuracy. Special Method of Suspending and Displacing Plateholder. — 
The spectrometer is described in detail in the preceding article. A special method 
of suspending the plateholder and giving it a known displacement is described, by 
which it is possible to fix the limit of accuracy directly. An X-ray bulb of the gas 
type was used with a specially designed anode which could be rotated so as to bring 
different parts of its face under the action of the cathode stream. The two kinds of 
lead were placed on different parts of the same anode. The uranio-lead was from 
a primary uraninite from India. 

Upper Half of Line from One Lead and Lower Half from Other Photographed on 
Same Plate. — The ai line of one kind of lead was photographed on the upper half 
of the plate, and the same line from the other lead on the lower half, immediately 
below it. Full lines for reference were sometimes photographed near the half 
lines for measurement purposes. The limit of accuracy was found by giving the 
plate a known displacement between the taking of one half and the other, of a 
line from the same kind of lead. 

Lai Lines from Ordinary and Uranio-lead Do Not Differ in Wave-length by as much 
as 0.005 Per Cent, — It is found that a displacement between two half lines of (10) "• 
mm. can be readily detected and that the wave-lengths of the Lax lines of the two 
kinds of lead can not differ by as much as 0.6 X (10) ~* A., or 0.005 per cent. 

Introduction. 

A KNOWLEDGE of the relation between the spectrum of a substance 
and that of its isotope is important in that it may throw further 
light on the structure of the atom. Some work in this line has been 
done. Aronberg,^ working with a grating spectrograph, has reached the 
conclusion that the wave-length of the line X 4058 is greater by 0.0043 A. 
for lead of radioactive origin than it is for ordinary lead. The work of 
Aronberg has recently been corroborated by Merton,* working with a 

> Aronberg, Astrophysical Jour., Vol. 47. p. 96. 1918. 

« Merton, Proc. Roy. Soc., No. A, 679, Vol. 96, p. 388, 1920. 



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328 C. D. COOKSEY AND D, COOKSEY. ^SSu 

Fabry and Perot italon. The X-ray spectra of lead isotopes have been 
investigated by Duane and Shimizu,^ and by Siegbahn and Stenstrdm.* 
The former authors, using an ionization method, measured the three 
critical absorption wave-lengths in the L-series from a specimen of 
ordinary lead and one of radio-active lead, the atomic weights of which 
had been determined by Richards and found to differ by more than 
\ per cent. They conclude that these wave-lengths do not differ be- 
tween the two kinds of lead by more than o.i per cent, or about 0.0008 A. 
Siegbahn and Stenstrom used a photographic method and investigated 
all the lines in the L-series, and the strongest lines in the M-series of 
ordinary and radioactive lead. The spectra of the two kinds of lead 
were photographed on the same plate under the same conditions. By 
using a lead screen to cover one part or another of the plate at a timet 
the middle portion of the lines of one kind of lead were obtained with 
the upper and lower portions of the lines of the other kind of lead above 
and below. The authors conclude that the wave-lengths of the two kinds 
of lead do not differ by more than 0.0005 A. They do not, however, in 
the article referred to, state how they estimated their limit of accuracy. 
The dispersion and width of slit used are not mentioned. For a descrip- 
tion of their apparatus they refer to a number of the Jahrbuch der 
Radioaktivitat und Elektronik for 1916 which, up to the present, has 
not come to hand on account of the war. 

Some time ago Professor Uhler suggested to the senior author that it 
would be of interest to investigate the X-ray spectra of isotopes, and as 
we had a supply of uranio-lead at our disposal, it was decided to undertake 
the work. On account of delays caused by the war we did not receive 
notice of the work of Siegbahn and Stenstrom until our work was well 
under way. The question of the spectra of isotopes seemed, however, 
of sufficient importance to warrant a repetition of the work by indepen- 
dent investigators even though the methods used by each were nearly 
the same. At the same time we had reason to believe that we could 
attain a sufficient degree of accuracy to detect a difference of wave-length, 
if present, well within the limits set by the authors named. We therefore 
decided to complete the work. 

The potential required to produce the K-series of lead is so high that 
it is doubtful if this series can be produced in the ordinary gas type tube. 
On the other hand the wave-lengths of the L-series are long enough to 
make the absorption of the air an appreciable factor. Not having a 
vacuum spectrometer at our disposal we decided to confine our investiga- 
tion to the ai line of the L-series of lead. 

1 Duane and Shimizu, Proc. Nat. Acad. Sci., No. 6, Vol. 5, p. 198, 1919. 
« Siegbahn and Stenstram, Phys. Zeitschr., Vol. 18, p. 547. ipi?- 



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No*^^^'] ^^^^ FREQUENCY SPECTRA OF LEAD ISOTOPES. 329 

The Lai line of lead is very broad and more resembles a band than a 
line. This is probably a characteristic of the lines of the L-series in 
general. A line of this nature will always be broader than the slit even 
when the plate is placed exactly at the focus of the slit, and the higher 
the dispersion, the greater will be this difference. The smallest difference 
in position between two such lines, taken in a manner similar to that 
described by Siegbahn and Stenstrom,^ which can be detected will depend 
on the narrowness, sharpness, and intensity of the lines. Since these 
fall off as the dispersion is increased there is nothing to be gained by 
carrying the dispersion beyond a certain point. 

If a photographic plate is so placed on the spectrometer that its plane 
is normal to the collimating line, and at such a distance from the axis of 
rotation of the spectrometer that the portion of the plate that is to 
receive the spectral line is either at the focus of a single slit, or some- 
where between the foci of two slits of equal width, then it is easily shown 
that the distance, 6-, between the axes of two lines whose difference in 
wave-length, AX, is small, is given by: 

rAX 



6 = 



d cos cos 20 * 



where r is the distance from the axis of rotation to the plate, measured 
along the reflected ray, d is the grating space of the crystal, and is the 
glancing angle. For the Lai line of lead and the (100) planes of calcite, 
is approximately 11.^18 and d is 3.03 A., which gives 

AX = 2.8A.(*). (I) 

The smallest difference in wave-length that can be detected is therefore 
directly proportional to the smallest detectable value of 6, and inversely 
proportional to r. Stated in this way however, and for the line under 
consideration, d is some direct function of r, and it becomes more im- 
portant to reduce 5 to a minimum than to increase r. 

Apparatus. 

We used a spectrometer, a detailed description of which will be found 
in the preceding article. The plateholder was always mounted in such 
a manner that its plane was approximately normal to the line of collima- 
tion and at such a distance from the axis of rotation that the part of the 
plate where the spectral lines were produced was always either at the 
focus of one or other of the slits Si and 52, or between these foci. 

For the special purpose of this experiment we mounted a screen 

« Loc, cit. 



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330 C. D. COOKSEY AND D. COOKSEY. [|S»2! 

directly in front of the plateholder, but not touching it. The screen 
consisted of a horizontal strip of brass about 1.7 mm. thick, of about the 
same length, and a little more than half the breadth of the opening in 
the front of the plateholder. The screen was supported by uprights, 
which stood on the same masonry pier with the spectrometer, but which 
were otherwise entirely independent of the latter. It could be raised 
entirely above the opening in the plateholder, or lowered so as to cover 
either the upper or lower half of this opening as desired. 

For a purpose to be explained later, the plate holder, instead of being 
supported on the azimuth circle clamped to the T rail, could be hung on 
two parallel wires of equal length, one fastened at each end of the top 
of the plateholder. The wires were about 134' cms. long, and their 
upper ends were fastened to a beam above the spectrometer. When the 
plateholder was supported in this way its regular mounting was removed 
from the T rail. In place of this the plateholder had screwed to its base 
a brass plate with two vertical posts extending below it and about 10 cm. 
apart. Through the lower end of each post and normal to the plane of 
the plate extended a screw with a smooth rounded point. By suitably 
adjusting the supporting wires, a small component of the weight of the 
plateholder served to make these screws bear gently against a smooth 
glass plate clamped to the T rail. The frame of a spherometer was 
clamped to one end of the T rail so that the axis of the screw was parallel 
to the long axis of the photographic plate, and the point of the screw 
bore against a smooth glass plate fastened on the end of the plate holder. 
The spherometer screw had a pitch of 0.5 mm. and its circular scale 
had a least count of o.ooi mm. To facilitate turning the screw accurately 
through one division of the head without rocking it in its nut, a tangent 
screw was provided. 

For diffraction grating we used the cleavage planes of a specimen of 
calcite crystal which had already been found to give very satisfactory 
lines. 

The X-ray bulbs were of the gas type and were made especially for us 
by Mr. A. Greiner, vice-president of the Green and Bauer Company, 
Hartford, Conn.; and the skillful manner in which he followed our 
design greatly facilitated the experimental manipulation. The one from 
which we obtained the fianl results had a water-cooled anode which 
could be rotated or removed by means of a ground glass conical joint. 
The anode was a copper disc with a silver disc about 2 mm. thick screwed 
to its face. The plane of the anode was made as nearly normal as possible 
to the axis of revolution of the ground glass cone. The anode was so 
mounted that its face made an angle of about 45° with the cathode rays. 



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No^4^^'] ^^^^ FREQUENCY SPECTRA OP LEAD ISOTOPES. 33 1 

and so that different parts of its face came under the action of these rays 
when the ground joint was rotated. A short side tube was sealed to the 
main bulb so that the axis of the tube was normal to the plane containing 
the cathode rays and the axis of the ground joint. The end of this side 
tube was covered by a brass plate with a small hole in it. The hole, in 
turn, was covered with aluminum foil about 0.12 mm. thick. The line 
through this hole to the focal spot made a small angle with the plane of the 
anode. 

The X-ray bulb was placed with the aluminium window close to the 
sjit, 5i, of the spectrometer, with the plane of the anode vertical, and 
so that the line from the focal spot through the aluminium window 
should be as nearly horizontal as possible. It was supported on three 
very rigid supports clamped to the anode tube, cathode tube, and an 
extra side tube respectively. These supports were fastened to the 
same table on which the spectrometer rested. This table consisted of 
a heavy granite slab cemented on a brick pillar isolated from the building. 

The specimens of lead to be compared were both placed on the anode 
at the same time in the following manner. The position of the focal 
spot on the anode was marked by running the bulb; the ground joint 
was then turned through about 45**, and the new position of the focal 
spot marked. The positions of the ground joint corresponding to these 
two positions of the anode were marked on the outer end of the cone. 
The anode was then removed from the bulb, and the silver disc taken off. 
A cluster of small holes, as close together as possible, was drilled in the 
silver at both positions of the focal spot. The holes were about i mm. 
in diameter, and enough were drilled to more than cover the focal spot. 
One of the kinds of lead to be investigated was pressed into one cluster of 
holes, and the other kind into the other cluster. Great care was taken 
not to contaminate either lead with the other. 

The pressure within the X-ray bulb, while running, was maintained 
as nearly constant as possible by a mercury diffusion pump so that the 
bulb would back a 12.7 cm. parallel spark gap. The current through 
the bulb was about 5 milliamperes, supplied by an ** Ideal Interrupterless " 
X-ray current generator, purchased from the Kny-Scheerer Company of 
New York City. 

The specimen of ordinary lead was cut from ordinary commercial 
sheet lead taken from the stock in the laboratory. The uranio-lead was 
very kindly prepared and furnished by Professor B. B. Boltwood with 
the statement that it was obtained from some lead chloride that had been 
separated from a primary uraninite from India; that it should be entirely 
free from ordinary lead, and should contain only a little "thorio-lead," 
if such a substance exists. 



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332 c. d. cooksey and d. cooksey. ^^! 

Method of Comparing Spectra. 

The method employed to compare the spectra of the two leads was 
as follows. The plateholder was placed on its usual mounting on the 
T rail, and one half of its breadth covered by the brass screen. It was 
then exposed to the rays from one kind of lead, the crystal always being 
given a small rotation back and forth around the position which gave 
the maximum reflection. At the end of the exposure the anti-cathode 
was turned until the other kind of lead came under the focal spot, and 
the plate exposed again with its other half covered by the screen. On 
some plates a full line was taken on each side of the half lines and about 
2 mm. from them. This was to give fiducial lines from which to measure. 
Plates were taken at various distances from the axis of rotation of the 
spectrometer and with various distances between this axis and the slit Si. 
The distance from the axis to slit S^ was always 4.5 cms. Different 
widths of slit were tried, and sometimes one, and other times two slits 
were used. 

The plane of the anode did not remain absolutely fixed when the ground 
joint was turned to bring one or the other lead under the focal spot, 
though the variation was very slight. However, when using two very 
narrow slits a long distance apart, it was necessary to realign the spec- 
trometer after turning the anode. This could easily be done by rotating 
the base of the spectrometer about the long axis of Si as described in the 
previous article. The spectrometer was lined up for one kind of lead 
and the position of the base noted. The other kind of lead was then 
brought into position, and the spectrometer realign for it. The first 
half line was then taken without changing the anode. Then, after the 
first kind of lead had been brought back into position, an auxiliary plate 
was introduced close to 52 and a series of exposures of equal length 
taken on it for different recorded positions of the spectrometer base 
around the position which had been noted. The position which gave 
the most intense image of 52 was then used in taking the second half ine. 
Absolutely no part of the spectrometer, slits, crystal or plateholder, 
were ever touched from the time the exposure for the first half line was 
started till the exposure for the second half was completed, except to 
rotate the base of the spectrometer to adjust the line up. This was 
done by slow motion screws, the base resting at two points on plane 
surfaces and pivoted at a third point on a carefully made cone. The 
auxiliary plate was supported without touching any part of the spec- 
trometer. 



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no*^^*] ^^^^ frequency spectra of lead isotopes, 333 

Test for Limit of Accuracy. 
We wished, if possible, to compare the spectra of the two kinds of 
lead to a much higher degree of precision than had previously been 
attained. We were therefore confronted with the problem of finding 
what was the smallest displacement that we could detect between two 
half lines taken in the manner described. To do this we proposed to 
give the photographic plate a known displacement after taking one half 
line and before taking the other, both halves being produced by the same 
kind of lead. Various means of supporting and displacing the plate- 
holder were tried for this purpose and proved unsatisfactory. Finally, 
at the suggestion of Professor Uhler, we hung the plateholder on wires 
in the manner already described and displaced it with the spherometer 
screw. 

Results. 

I. Limit of Accuracy. — ^Two plates, nos. 41 and 44, were taken with 
the plateholder suspended on the wires. Slit Si was wide open, and Si 
was 0.02 mm. wide. The value of r, equation (i), was 4.5 cms. The 
crystal was rotated back and forth through an angle of i J' on each side 
of the best setting. On No. 41 five exposures were taken using the 
uranio-lead only. The first exposure was a full line, the third and 
fourth were upper halves, and the second and fifth were lower halves. 
The plateholder was displaced by the screw in the same direction after 
each exposure; 2.000 mm. after the first, 0.002 mm. after the second, 
2.000 mm. after the third, and 0.004 nmi. after the fourth. On No. 
44 only four exposures were taken, using the ordinary lead. The first 
and fourth were full lines, the second was a lower, and the third an 
upper half. The displacements after the first and third were both 
2.000 mm., and that after the second was o.ooi mm. 

Both the small displacements between adjacent half lines on plate 
No. 41 were quite obvious under a low power magnifying glass. The dis- 
placement of O.OOI mm. on No. 42 was not visible in this manner. The 
lines on both plates were sharp and black and not more than 0.025 mm. 
broad. Both plates were measured on a measuring engine, frequently 
tested and regularly used by Uhler and others for measuring plates 
obtained with the large Rowland spectrograph. The measurements 
were made along two lines normal to the spectral lines, one a small 
distance above the break between the halves and the other the same dis- 
tance below. The measured values of the distances agreed very closely 
with the actual displacements. The values of the small displacements, 
obtained by subtracting the upper from the lower distances, in no case 
differed from the actual displacements by as much as o.ooi mm. We 



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334 ^' ^' COOKSEY AND D. COOKSBY. [iSSS 

therefore feel justified in assuming that with lines of the sort obtained 
on these two plates, a displacement of o.ooi mm. could not escape 
detection. 

2. Comparison of Leads. — ^The following plates were taken with two 
exposures, giving the upper half of the line from one lead and the lower 
half from the other, on each, the plateholder remaining fixed during the 
two exposures, and the crystal rotated back and forth around the best 
setting. 

Plate No. 6. — The width of Si was 0.04 mm., and Si was wide open. 
The distance from Si to the axis of rotation was 35 cms. and the value 
of r was 35 cms. The ordinary lead line was above, and the uranio-lead 
line below. The lines were very fuzzy, though dark, and about o.i mm. 
broad. 

Plate No. 7. — ^The data for this plate are the same as for No. 6 except 
that Si was closed to 0.02 mm. and the positions of the lines from the 
two leads were reversed. The lines were not quite as broad as on plate 
No. 6, but were weaker and just as fuzzy. 

Plates No. 29 and No. 30. — ^The width of both Si and 52 was 0.02 mm. 
The distance of Si to the axis of rotation was 20 cms. and the value of r 
was 20 cms. The positions of the lines were reversed on the two plates. 
The lines were narrower than on the other two plates and were fairly 
strong, but were still too broad and fuzzy to permit of precise measure- 
ments. 

None of these plates showed any displacement between the lines, but 
their axes were too indefinite to permit of their being compared with a 
high degree of precision. An attempt was made to set a superior limit 
to the displacement that could exist without being visible. These plates 
were placed on the measuring engine, and one cross hair of the microscope 
was set as nearly as possible parallel to, and on what appeared to be the 
axis of the pair of half lines considered as one continuous line. The 
engine screw was then turned the least amount that would throw the 
cross hair, beyond question, off the axis of the lines. In this manner it 
was estimated that, on the first two plates, there could not have been a 
displacement as great as 0.02 mm., and on the second two, as great as 
o.oi mm. If these values are assigned to 8 in equation (i), with the 
corresponding values of r , it is seen that the possible difference of wave- 
length between the lines of the two kinds of lead can not exceed 1.6 (10)"^ 
A. on the first two plates, and one half this value on the second two. 

In order to have lines which could be measured with as high a degree 
of accuracy as those obtained in the tests for the smallest detectable 
displacement, we took two more plates, No. 46 and 47. The conditions 



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Vol. XVI.l 
No. 4. J 



HIGH FREQUENCY SPECTRA OF LEAD ISOTOPES, 



335 



under which these plates were taken were as follows. Both slits were 
0.02 mm. wide. The distances from Si and S^ to the axis of rotation 
were 15.6 cms. and 4.5 cms. respectively. The value of r was 4.9 cms. 
The crystal was rotated back and forth through an angle of i J' on each 
side of the best setting. Four exposures were taken on each plate, 
namely: a full line A was taken for one kind of lead, the plateholder was 
displaced along the T rail about 2 mm., and the lower half, 5, of the line 
from the same kind of lead was taken; the plate holder remaining fixed, 
the upper half, C, of the line from the other kind of lead was taken, and 
then the plateholder was displaced about 2 mm. further and a full line, 
X), from the same lead as C, was taken. The direction of the displace- 
ment of the plateholder was such as to place A on the long wave-length 
side of B and C, and D on the short. 

Table I. 

Plate No, 46, 



Upper Half. 


Lower Half. 


iAQ, 


(AD), 


(.CD). 


(AB). 


(AD), 


(BD), 


2.1355 
.1341 
.1370 
.1358 
.1363 


4.2021 
.2033 
.2038 
.2059 
.2043 


2.0666 
.0692 
.0668 
.0701 
.0680 


2.1384 
.1373 
.1356 
.1363 
.1357 


4.2038 
.2051 
.2035 
.2061 
.2048 


2.0654 
.0678 
.0679 
.0698 
.0691 


Mean 2.1357 


4.2039 


2.0681 


2.1367 


4.2047 


2.0680 



(AB) - (ilO « 0,0010 

(CD) — (BD) « o.oooj 

Mean ■» 0.0006 



Plate No, 47' 



Upper Half. 


Lower Half. 


(AC), 


(AD). 


(CD). 


(AB). 


(AD). 


(BD). 


2.0020 


4.0512 


2.0492 


2.0045 


4.0534 


2.0489 


.0045 


.0522 


.0477 


.0075 


.0550 


.0475 


.0044 


.0522 


.0478 


.0021 


.0538 


.0517 


.0064 


.0550 


.0486 


.0046 


.0539 


.0493 


.0036 


.0524 


.0488 


.0057 


.0533 


.0476 


.0031 


0.517 


.0486 








Mean 2.0040 


4.0525 


2.0485 


2.0049 


4.0539 


2.0490 



(AB) - UO - o.oooQ 

(CD) — (BD) « — 0.000 s 

Mean ■■ 0.0002 



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336 C. D. COOKSEY AND D, COOKSEY, [^2S 

On plate No. 46 the lines A and B were produced by uranio-lead and 
the lines C and D by ordinary lead. On plate No. 47, on the other hand, 
the lines A and B were produced by ordinary lead, and C and D by 
uranio-lead. The lines on both plates were well defined and sharp 
though not quite as black as on plates 41 and 44. The upper and lower 
halves of each plate were measured on the engine. These measurements 
are set forth in detail in Table I., the figures in each column being the 
various measurements of the distance between the two lines corresponding 
to the letters at the head of the column. The units are approximately 
millimeters. 

It will be seen from the table that on plate No. 46 the measurements 
from both A and D assign to C, an ordinary lead line, a longer wave-length 
than Bj a uranio-lead line. The measurements from A on plate No. 47, 
however, assign to C, a uranio-lead line, a longer wave-length than B, 
an ordinary lead line, while the measurements from D reverse this 
order. None of the displacements between the half lines deduced from 
the measurements of these plates are greater than o.ooi mm., and the 
means are much less. Obviously the conclusion to be drawn from these 
two plates is that there is no difference in wave-length between the two 
kinds of lead great enough to produce a shift in the line of as much as 
O.OOI mm. With the value of r used with these plates we feel justified 
in the conclusion that the difference in wave-length between ordinary 
and uranio lead for the ai line of the L-series can not be as great as 
0.00006 A. The wave-length of this line being about 1.18 A., the dif- 
ference, if it exists at all, must be less than 0.005 per cent. 

In conclusion it gives us great pleasure to express our sense of obligation 

to Professor Uhler for his interest and many valuable suggestions in 

connection with the work, and to Professor Boltwood for supplying us 

with the specimen of uranio-lead used. 

Sloane Physics Laboratory, 
Yale University, 
Maich 21, 1920. 



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Na'4?^^^*] VARIATION OF THE FACTOR h, 337 



ON THE VARIATION OF THE FACTOR h IN THE EQUATION 

\mifl — hv. 



By Fernando Sanford. 



Synopsis. 



Relation between the fi- and y-rays of Ra B; Theory. — The author has previously 
shown that by combining the equations for orbital motion of an electron about a 
central positive charge with the equation imt^ •« /tv, the magnitude of the central 
positive charge about which a radiating electron is revolving may be calculated, and 
that when this value of the central charge is equated with one derived from an 
equation of the form of Moseley's equation for the frequency of X-rays the wave- 
length of the shortest lines in the K-radiation of elements of atomic numbers from 35 
to 58 may be calculated as accurately as they can be measured. Later measure- 
ments of wave-lengths of elements with higher atomic numbers show that the 
computed wave-lengt hs vary progressively from the measured wave-lengths as the 
atomic numbers increase. It is also known that Moseley's law for the frequency of 
X-rays varies in the same manner. 

The equation from which the author calculates the wave-length is 

Since the right-hand member of this equation shows that the nuclear charge in the 
case of K-radiation increases by 2e in passing from one element to the one of next 
higher atomic number, it is not probable thai this law breaks down at atomic 
number 58, and that the nuclear charges of elements of higher atomic number increase 
by variable quantities. The failure of the equation to apply to elements of higher 
atomic number must then be looked for in the left-hand member. In this member 
the only variable quantities (since X is measured) are m, the mass of the electron, and 
possibly h, the Einstein factor. These quantities appear in the form of the ratio AV^t 
and the author has calculated values of h*/m which substituted in his equation 
will give the correct wave-lengths for elements of higher atomic number. These 
values of h*lm are then plotted against their corresponding wave-lengths and a smooth 
curve is obtained. Values of h*/m are then taken from this curve for a number of the 
7-ray wave-lengths measured by Rutherford and Andrade. These wave-lengths 
are then assigned to certain groups of j9-rays from Radium B on grounds which 
seem to the author permissible. The mass, m. and the quantity h corresponding to 
the speeds of these fi particles were then computed. The values of h computed in 
this way seem to be derivable from m by the equation h « 4.25 log m -h 2.50' lo"*'. 
Using this value of h, wave-lengths were computed for the fourteen groups of jS-rays 
from Radium B whose speeds were measured by Rutherford, and nine of them 
were found to agree satisfactorily with wave-lengths in the 7-radiation of Radium 
B and Radium C. while two more of the measured wave-lengths seem to correspond 
with the speeds of j8-particles from Radium C. 

Calculation of Orbital Velocities of Radiating Electrons by Substituting 4,25 log m 
+ 2,50* 10"^ for h in the equation }m»* = hv. 

Using a series of values of v from o.i*io" to 2.2-10" corresponding values of 



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338 FERNANDO SANFORD, [llSSf 

m were calculated f rom Bucherer's equation for the transverse mass of an electron, 
viz., m ■» mo/Vi — f^/c«. From these values r was computed using the equation 
p a irm^l(4.2S log m + 2.50), and these values of p were plotted on a large scale 
as abscissas using the values of v from which they were derived as ordinates. From 
this curve were taken values of v corresponding to all the highest frequencies of K- 
radiation as measured by Siegbahn and his colleagues and Duane and his colleagues. 
The values of v obtained in this way are then compared with values calculated from 
the equation v = 2.0S4(Ar — 1.66) and are found to agree satisfactorily with no 
tendency to vary progressively with the higher numbers, as do the values calculated 
by Duane using A as a constant. 

It is concluded that since h may be replaced in the equation imi^ ^ hp by a func- 
tion of m with a great improvement in the accuracy of the equation, there is no longer 
ground for speaking of an Energy quantum in this equation. 

THE writer has shown elsewhere^ that by combining the equation for 
orbital motion of an electron about a central positive charge, viz., 
tnv^/R = QelB}, with the equation \mv^ = hv it is possible to compute 
the central positive charge, Q, of a radiating atom, and from this value 
'of Q and a corresponding value computed by an equation of the form 
given by Moseley to determine the wave-lengths of all known character- 
istic X-ray bands. Also, by combining the equation for Q with the 
formulae for computing the wave-length of the lines in the various 
spectral series it was shown that the unit electrical charge may be com- 
puted from any line in any known spectral series of hydrogen or helium 
in terms of the wave-length and the serial number of the line. It is also 
possible by the use of the same equation to calculate the value of the 
Einstein factor h from the convergence charge of the Balmer series in 
hydrogen. 

The above mentioned computations are not based upon any theory of 
atomic structure except that radiating electrons are in orbital revolution 
about a central positive charge, and that the frequency of revolution of 
the electron determines the wave-frequency of its radiation. In the 
opinion of the writer these assumptions are not incompatible with any 
of the commoner theories of atomic structure, but are admittedly in 
conflict with the Bohr theory of radiation. 

The expression for the value of the central charge, Q, derived from the 
above equations is 

^1/2^8/2^1/2 

By equating this value of Q with a value derived from an equation 
of the form of the Moseley equation we may get an expression for the 

» See especially On The Nuclear Charges of Atoms. Physical Review, IX.. 383 (1917); 
The Astronomical Atom and the Spectral Series of Hydrogen. Astrophysical Journal. XLVIII., 
I (1910); The Helium Spectrum and the Unit Electrical Charge, Astrophysical Journal, 
XLIX., 337 (1919). 



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Na"4?^^^*] VARIATION OF THE FACTOR A. 339 

value of X. Thus for the characteristic K-radiation Q = 2e{N — 3.6) 
where N is the atomic number. Then for this radiation 

^^^ji^,- = 2e{N - 3.6). 

This equation has been found to apply to the elements from iV = 35 
to iV = 58 so that the wave-lengths of the K-radiation from these 
elements may be calculated from this formula as accurately as they 
may be measured.^ 

In the Physical Review of January, 1920, the present writer under- 
took to show that if the speed of the jS-particles sent off from Ra-B and 
Ra-C is related by Einstein's law to the accompanying 7-radiation then 
before the expression ^tnv^ may be substituted for Ve in that equation 
the factor h, as well as m, must be assumed to vary with the speed of the 
i3-particles. 

Since the article referred to was written, two papers which have an 
important bearing on this question have appeared. In the Physikalische 
Zeitschrift of June i, 1919, Siegbahn and Jonssen have published new 
determinations of the wave-lengths of highest frequency in the K- 
radiation series of a considerable number of elements from cadmium to 
uranium, and in the Physical Review of December, 1919, Duane and 
Hang-Fuh-Huh and Duane and Shimizu have extended the wave-length 
measurements on the absorption frequencies of the K-radiation to ele- 
ments of both lower and higher atomic numbers than those whose fre- 
quencies were determined by Blake and Duane. These measurements 
when taken with the wave-length determinations of Siegbahn and 
Stenstrom in 1916 give a series of measurements of the short wave-lengths 
in K-radiation for most of the elements from atomic numbers iV = 12 
to N = 92. 

When these newly determined wave-lengths are compmted by our 
formula it is found that the correspondence is equally as good as for the 
measurements of Blake and Duane up to an atomic number 58, but that 
from this point onward the calculated values are greater than the 
measured values. Siegbahn and Jonssen call attention to the fact that 
from this point onward their wave-lengths do not follow Moseley's 
law, and they attribute the variation from this law to the variable mass 
of the electron at high speeds. 

In the papers in the Physical Review, Duane and his colleagues 
calculate a value of v for each of the elements whose wave-lengths they 
have measured by using the equation ^mr* = hv and computing the 
value of m at each speed by the Bucherer equation, m = Wo/ Vi — (v^jc^), 

» See Physical Review. XV., 68 (January. 1920). 



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340 FERNANDO SANFORD, [^SS 

They found that their values of v computed in this way bore a straight 
line relation to the atomic numbers, as does the square root of the 
frequencies in Moseley*s equation, but that for atomic numbers above 58 
their calculated values of v vary slightly, but progressively, from the 
values given by the atomic number relation. 

It will be seen that in the equation 
2ii2Hmcm ' 

^.X^-^e. = ''^^ - 3.6) 
a variation in m can affect only the left-hand member of the equation, 
and that the only other quantity in this member which may possibly 
vary (since X is measured) is the quantity A, or, in other words, the 
possible variable quantity in this member is the fraction ¥lni. Since 
the right-hand member of the equation merely shows that Q increases by 
2e in passing from any element to the one of next higher atomic number, 
there is no reason for thinking that this law changes and that the increase 
of charge becomes variable for elements of higher atomic number than 58. 

If we may rely upon the constancy of the right-hand member of the 
equation, we may compute values of h^/tn for each of the given wave- 
lengths and perhaps decide whether the variation in this side of the 
equation is due wholly to w, or whether h is also probably variable. 

In Table I. Blake and Duane's wave-length measurements are given 
in the third column, those of Siegbahn and Jonssen in the fourth column, 
the wave-lengths calculated from our formula in the fifth column and the 
values of h^/m required to give the measured wave-lengths in the sixth 
column. It may be seen that h^/m remains constant to within the 
errors of measurement to about N = 58, from which point on it decreases, 
while the calculated values of the wave-length also show a systematic 
variation from about the same value of N, 

When these values of hz/tn are plotted as ordinates against their 
corresponding wave-lengths as abscissas a smooth curve is obtained from 
which values of A'/m may be taken for any wave-length down to 
X = 0.1 • io~^. If corresponding values of v could now be found it would 
be possible to calculate the respective values of h. This I have attempted 
to do in the following way : 

All of the wave-length calculations and the values of A^/m given in 
Table I. are based upon the assumption that the speeds of electrons 
expelled under the stimulus of ultra-violet light or of X-rays are the 
orbital speeds which they possessed at the instant of breaking away from 
their respective atoms. If this be the true explanation of their velocities, 
it seems almost certain that the same explanation must account for the 
speeds of the jS-particles expelled by radioactive bodies. This would 



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Vol. XVI.1 
No. 4. J 




VARIATION OF THE FACTOR h. 


341 






Table I. 






BlsnMiit* 


N. 


Xxo>, B. A D. 


Xxo>, S. A J. 


Xxo>, Calc. 


h^lm, xoM. 


Br 


35 
37 


.9179 
.8143 




.924 
.817 


309.5 


Rb 


310.5 


Sr 


38 
39 
40 
41 


.7696 
.7255 
.6872 
.6543 




.771 
.727 
.689 
.654 


311 


Yt 


309.5 


Zr 


311 


Nb 


311 


Mb 


42 


.6180 




.618 


311 


Ru 


44 


.5584 


f 


.558 


311 


Rh 


45 


.5324 




.532 


311.5 


Pd 


46 


.5075 




.507 


312.5 


Ag 


47 


.4850 




.484 


312 


Cd 


48 


.4632 ' .4629 


.463 


312 


In 


49 
50 
51 
52 
53 
55 
56 


.4434 
.4242 
.4065 
.3896 
.3737 
.3444 
.3307 


.4231 

.3877 
.3715 
.3436 
.3306 


.443 
.424 
.409 
.389 
.373 
.345 
.332 


312 5 


Sn 


312 


Sb 


312 


Te 


310.5 


I 


310.5 


Cs 


310.5 


Ba 


310.5 


La 


57 
58 
59 
60 


.3188 
.3073 


.3186 
.3064 
.2946 
.2835 


.320 
.308 
.297 
.286 


310.5 


Ce 


310.5 


Pr 


309 


Nd 


308 


Sa 


62 
63 




.2636 
.2543 


.2665 
.2585 


307.5 


Eu 


306.5 


Gd 


64 




.2456 


.2495 


306.5 


Dy 


66 




.2294 


.234+ 


305.5 


Ho 


67 




.2214 


.2265 


304.5 


Pt 


78 
79 




.1578 
.1524 


.165 
' .1605 


298.5 


Au 


296.5 


Hg 


80 




.1479 


.156 


295 


Tl 


81 
82 




.1427 
.1385 


.152 
.148 


292 


Pb 


291.5 


Hi 


83 
90 




.1346 
.1127 


.1445 
.122 


290 


Th 


288 


U 


92* 




.1048 


.1167 


280 











require that the Einstein photoelectric equation should hold for the 
energies of the jS-rays and the frequencies of the accompanying 7-radia- 
tions from the same elements. Rutherford and his colleagues have 
given much time to the investigation of this question, and are of the 
opinion that such a relation does, indeed, hold and that some of the 
7-rays from Ra-B and Ra-C are the true K- and L-radiation bands of 
these elements. 

In an article on The Connexion Between /3 and 7 Ray Spectra^ Ruther- 

» Phil. Mag., 28, 305-319. 



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342 FERNANDO SANPORD. gj 

ford gives the velocities relative to the velocity of light of fourteen 
groups of /3-rays expelled from Ra-B and ten groups of /3-rays from Ra-C. 
In an article by Rutherford and Andrade on The Spectrum of the Pene- 
trating y Rays from Radium B and Radium C in the same volume of the 
Philosophical Magazine is given a table of the wave-lengths of fourteen 
different lines in the 7-ray spectrum of these elements. The authors do 
not know to which element the various lines belong, but give their reasons 
for believing that the shortest wave-lengths are due to Radium C, and 
that the lines X = 1.59' lO"* and X = 1.69 -lO"* are the characteristic 
K-radiation lines of Radium B. 

In the data on the velocities of jS-rays the groups of rays of speeds 
1. 905-2. 100 are marked very strong, indicating that there are more 
j8-rays of this speed than of any other unless it be i.oi. Since the lines 
of wave-length 1.59 and 1.69 are referred to as the strongest lines in the 
7-ray spectrum, it seems reasonable to assign these lines to the group of 
j8-rays whose speeds are from 1.9 to 2.10- iO"^°. 

If we calculate a value of w for a speed of 1.9-10"^° we find 
tn = i.i6-io~*^. Since the wave-length 1.69 lies within the spectral 
region for which we have computed the value of A'/w, we may take the 
value of this ratio from the curve, which was drawn for that region, 
where we find it to be 300-10"^. Accordingly, A* = 348 -lo"*^ and 
h = 7.03 lO"". 

In order to express graphically the relation of A to w we must have this 
relation at one more point, at least, since we already have the initial 
values of the two quantities. By a slight extrapolation of our curve 
it was seen that the 7-ray line X = .99 must give h^/tn = 276, approxi- 
mately. For trial purposes this line was assigned to the highest speed 
/3-particle from Radium-B, viz., v = 2.469. For this speed m = i .2 • lO"^, 
and if h^lm — 276, h = 7.60. 

When these three values of h and m were compared they seemed to 
suggest that h varies as log m. On plotting a curve with the values of h 
as abscissas and the values of log m as ordinates, a linear relation was 
seen to hold between the two quantities, so that for A- lo^^ and log m- 10^, 
h = 4.25 logw + 2.50* lo"". 

Assuming the validity of this equation it is possible to calculate w and 
h for each of the speeds given, and to compare the values of h^/m obtained 
in this way with values taken from our curve for each of the wave-lengths 
measured in the spectra of Radium B and Radium C. This is done in 
Table II., where the velocities of the jS-rays from Radium B are given in 
the first column, the corresponding values of m as computed from the 
equation m = mo/Vi — (r^/c^j in the second column, h as derived from 



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Vol. XVI.1 
No. 4. J 



VARIATION OP THE FACTOR h. 



343 



the equation h =4.25 log m + 2.50 in the third column and h*lm in the 
fourth column. In the fifth column are given values of. X corresponding 
to the values of h^/m in the fourth column as taken from the curve drawn 
to show this relation. In the sixth column are given the values of X as 
measured by Rutherford and Andrade in the 7-radiation of Radium B 
and Radium C. 

Table II. 



fi Radiation from Radium B. 


y Radiation. 


V. 


m. 


A. 


A*fm, 


XCalc. 


XMeas. 












.71 


2.469 


1.59 


7.60 


276 


.99 


.99 


2.450 


1.56 


7.55 


278 


1.03 




2.391 


1.49 


7.46 


281 


1.10 




2.361 


1.46 


7.45 


282 


1.15 


1.15 


2.286 


1.39 


7.35 


287 


1.24 




2.252 


1.36 


7.31 


288 


1.27 




2.193 


1.32 


7.25 


289.5 


1.31 




2.157 


1.295 


7.22 


292 


1.37 


1.37 


2.100 


1.26 


7.16 


292 


1.37 


1.37 


1.968 


1.195 


7.06 


297 


1.55 


1.59 


1.905 


1.165 


7.03 


300 


1.69 


1.69 
1.96 
2.29 
2.42 
2.62 






















1.278 


.995 


6.74 


307 


2.62 


1.242 


.990 


6.73 


308 


2.90 


2.96 
3.24 
3.93 
4.28 












1.011 


.956 


6.66 


309 


4.28 



A comparison of columns five and six of Table II. will show that nine 
of the fourteen measured wave-lengths correspond as closely as could 
be expected with the values calculated from the speeds of the )3-particles 
on the assumption that h =4.25 log m + 2.50. For the three slowest 
groups of j8-particles the values of h^/tn fall on a part of the curve 
where h^/m varies but slightly with the wave-length, and where the 
values of X derived from this curve must be more uncertain than for the 
faster j8-particles. 

The slowest speed given has been assigned to the wave-length 4.28 
from the following considerations: The radiation of particles at this 
speed is marked *'very strong/* indicating that this group of j8-particles 
corresponds to a characteristic radiation of the element. I have shown 
elsewhere^ that the shortest wave-length of the characteristic L-radiation 

* Electrical Charges of Atoms and Ions, Leland Stanford Junior University Publications, 
p. 70. 



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344 FERNANDO SANPORD. I^SSS? 

may be calculated from the equation 

r 2.882 IO-" 1« 
le{N-i5A)i 

for elements up to atomic number 71. This equation would give for 
Radium B (iV = 82) a wave-length X = 4.33, which is within the error 
of measurement the line 4.28. 

The measured speeds of the /3-particles from Radium C are with two 
exceptions much higher than those from Radium B, and the curve derived 
from X-ray wave-lengths may not safely be extrapolated far enough to 
give a probable estimate of their 7-ray wave-length. The slowest 
group of these particles has a velocity of 2.25-10^°, which would make its 
7-ray wave-length about 1.27 from our computation. The next slowest 
group of j8-particles has a speed of 2.604. This would give w = 1.80 
and h = 7.83, making h^/m = 266. This seems to correspond with 
the measured wave-length .71. 

It seems not improbable that the 7-radiation from the other j8-particles 
of Radium C was of too short wave-legth to be measured by Rutherford 
and Andrade. With their spectrometer the wave-length taken as .71 
was determined from a deviation of only 43', and the authors say, 
"It is surprising that the architecture of the crystal (rock salt) is suffi- 
ciently definite to resolve such short wave-lengths. This is especially 
the case when we consider that owing to the heat agitation of the atoms, 
the distance between the atoms must be continually varying over a 
range comparable with the wave-length of the radiation." 

In a paper by F. Dessauer and E. Back published in Berichte der 
Deutschen Physikalischen Gesellscahft, May 30, 1919, the authors give 
the results of their attempt to find the shortest wave-length given by 
X-rays from any element. By using a potential of 170 k.v. and an 
exposure of 9 hours they found the apparent limit of X-rays at 
X = .57 -lo"*. It is probable that all of the /3-rays from Radium C 
except the two sets referred to would be accompanied by 7-ray s of shorter 
wave-length than .57-10"*. 

If these estimates of the relation between the speeds of j8-rays and the 
wave-lengths of their accompanying 7-radiations are correct, it seems 
almost certain that the speeds of /3-particles are the orbital speeds which 
they possessed at the instant of escaping from the atoms. 

It also seems certain that for speeds as great as those of /3-particles 
the product imr* of the /3-rays does not bear a constant ratio to the 
frequency of the accompanying 7-radiation. 

It has already been mentioned that Duane and his colleagues have 



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NaV^^^*] VARIATION OF THE FACTOR h, 345 

calculated values of v from the K-radiation of a large number of elements 
which values are related to the atomic numbers by an equation of the 
form of Moseley's equation for the square root of the frequencies. It 
will be seen from our fundamental equation /or the atomic charge that 
this will necessarily be true if h^/tn is constant or bears a straight line 
relation to the atomic numbers. It was observed, however, that this 
law of Duane's holds only so far as the wave-length may be correctly 
calculated on the assumption of the constancy of h^/tn. 

In order to test the same relation with values of v calculated from 
our hypothesis, I have calculated values of m for a series of values of v 
from V = o.i • 10^® to r = 2.2 • I0*^ letting 

9io~" 

tn = . — . 

Vi - v^/c^ 

Then from the equation Jmv* = ^{4,25 log tn + 2.50) I have calculated 
values of v for each value of i; us^d in computing w. These values of v 
were then plotted on a large scale as abscissas against the respective 
values of V as ordinates. From this curve it is possible to obtain a value 
of V accurate to the third significant figure for any value of v from 
I' = 0.1 • 10" to V = 40- lo^*. 

Values of v corresponding to all the K-radiation frequencies measured 
by Siegbahn and Stenstrom, Siegbahn and Jonssen, Blake and Duane, 
Duane and Hang-Fuh-Huh and Duane and Shimizu were then taken 
from this curve and plotted against their respective atomic numbers. 
In the case of the Siegbahn and Stenstrom measurements the frequencies 
for the Kp lines were used throughout. It was found that the velocities 
calculated in this manner bear a straight line relation to the atomic 
numbers with no tendency to systematic departure on either side of the 
line for higher atomic numbers. This relation of velocity to atomic 
number may be expressed by the equation v = 2.054(iV^ — 1.66). 

The relation between the values of v calculated in the two ways is 
shown in Table III., in which the wave-length measurements of Siegbahn 
and his colleagues are given in the third column and those of Duane and 
his colleagues in the fourth column. The corresponding values of v are 
given in the fifth column. Where two values of X are available a mean 
value is used in computing v. The sixth column gives v from the 
equation 



V = /2y(4»25logm + 2.50) 



and the seventh column gives v from the equation v = 2.054(iV — 1.66). 
It will be seen that though the series runs to iV = 92, the agreement 



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346 



FERNANDO SANFORD, 



rSBCOMD 

LSssnt. 



Table III. 



-4 



2v(4,2S log m + 2.50 



' 2,0S4(N — 1,66), 



Element. 


A^. 


and Others. 


X Diuuieand 
Others. 


r. 


«i. 


vt. 


Mg 


12 


9.477 




.3165 


.213 


.2124 


Al 


13 


7.986 




.3753 


.233 


.233 


Si 


14 


6.759 




.4436 


.2535 


.2535 


P 


15 


5.808 




.516 


.274 


.274 


S 


16 


5.018 




.5978 


.295 


.2946 


CI 


17 


4.394 




.6826 


.316 


.3152 


K 


19 


3.449 




.8700 


.357 


.3564 


Ca 


20 


3.086 




.973 


.377 


.377 


Sc 


21 


2.778 




1.080 


.3975 


.3972 


Ti 


22 


2.509 




1.195 


.418 


.418 


Va 


23 


2.281 




1.315 


.437 


.438 


Cr 


24 


2.079 


< 


1.443 


.458 


.458 


Mn 


25 


1.902 


1.8892 


1.582 


.480 


.4795 


Fe 


26 


1.743 


1.7396 


1.721 


.500 


.500 


Co 


27 




1.6018 


1.86 


.520 


.521 


Ni 


28 




1.4890 


2.015 


.540 


.541 


Cu 


29 




1.3785 


2.175 


.560 


.562 


Zn 


30 




1.2963 


2.315 


.578 


.582 


Ga 


31 




1.1902 


2.521 


.602 


.603 


Ge 


32 




1.1146 


2.693 


.623 


.623 


As 


33 




1.0435 


2.875 


.644 


.644 


Se 


34 




.9790 


3.065 


.665 


.664 


Br 


35 




.9179 


3.268 


.685 


.685 


Rb 


37 




.8143 


3.684 


.726 


.726 


Sr 


38 




.7696 


3.898 


.745 


.746 


Yt 


39 




.7255 


4.136 


.767 


.767 


Zr 


40 




.6872 


4.365 


.788 


.788 


Nb 


41 




.6503 


4.61 


.808 


.808 


Mo 


42 




.6180 


4.855 


.830 


.829 


Ru 


44 




.5584 


5.374 


.871 


.871 


Rh 


45 




.5330 


5.63 


.891 


.890 


Pd 


46 




.5075 


5.913 


.912 


.911 


Ag 


47 




.4850 


6.185 


.9325 


.932 


Cd 


48 


.4629 


.4632 


6.48 


.953 


.952 


In 


49 




.4434 


6.766 


.973 


.973 


Sn 


50 


.4231 


.4242 


7.08 


.994 


.994 • 


Sb 


51 




.4605 


7.384 


1.014 


1.014 


Te 


52 


.3877 


.3896 


7.722 


1.036 


1.034 


I 


53 


.3715 


.3737 


8.065 


1.057 


1.055 


Cs 


55 


.3436 


.3444 


8.725 


1.098 


1.096 


Ba 


56 


.3306 


.3307 


9.08 


1.118 


1.116 


La 


57 


.3186 


.3188 


9.42 


1.138 


1.137 


Ce 


58 


.3064 


.3068 


9.80 


1.160 


1.157 


Pr 


59 


.2946 




10.18 


1.181 


1.178 



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Vol. XVI.1 
No. 4. J 



VARIATION OF THE FACTOR h. 



347 



FIfflBWitr 


N, 


X SiedMlm 
and Others. 


X Dnaaeand 
Others. 


9, 


r,. 


v%. 


Nd 


60 


.2835 


.2861 


10.54 


1.201 


1.199 


Sa 


62 


.2636 




11.38 


1.243 


1.239 


Eu 


63 


.2543 




11.79 


1.263 


1.260 


Gd 


64 


.2456 




12.21 


1.284 


1.282 


Tb 


65 




.2398 


12.51 


1.299 


1.301 


Dy 


66 


.2294 


.2308 


13.04 


1.324 


1.322 


Ho 


67 


.2214 




13.54 


1.348 


1.343 


W 


74 




.1786 


16.78 


1.485 


1.486 


Os 


76 




.1683 


17.82 


1.531 


1.528 


Pt 


78 


.1578 




19.01 


1.572 


1.568 


Au 


79 


.1524 


.1541 


19.57 


1.590 


1.589 


Hg 


80 


.1479 


.1501 


20.14 


1.608 


1.608 


Tl 


81 


.1427 




21.01 


1.640 


1.626 


Pb 


82 


.1385 


.1424 


21.35 


1.651 


1.650 


Bi 


83 


.1346 




22.29 


1.681 


1.671 


Th 


90 


.1127 




26.61 


1.814 


1.815 


U 


92 


.1048 




28.60 


1.866 


1.835 



between the two values of v is very close and no progressive variation 
appears. In only one case, that of uranium, is the difference between 
the two values of v as great as one per cent. From the equations here 
used the wave-length of the shortest K-radiation from uranium should 
be X = .1099 • I o~® instead of .1048' io~*, as given by Siegbahn and 
Jonssen. Deasauer and Back, in the paper already mentioned, attempted 
to find the wave-length of the Kfi line of uranium, and concluded that it 
lies between .104 -lo"* and .154' io~®. When extrapolated from their 
measured wave-length of the platinum line by Moseley's equation they 
found it to be between .114 and .136- lO""^, but it is well known that 
Moseley's equation does not apply closely to elements of the higher 
atomic numbers. From Sommerfeld's formula this line would lie be- 
tween .131 and .146- lO"*. 

The one other considerable deviation is in the case of thallium, for 
which our equation would give a wave-length .1455 -lo"* instead of 
.1427 'lO"*, as determined by Siegbahn and JSnssen. 

On the whole, the two values of v are in very satisfactory agreement 
when we take into consideration that the most careful wave-length 
determinations in this region by different experimenters frequently 
differ in the third decimal place. 

While it is probably too much to claim that the relations shown in 
Table II. and Table III. give an adequate test of the value of the expres- 
sion here substituted for h in the equation \fm^ = Av, they are, so far 
as is known to the writer, the only tests thus far made of the validity of 



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348 FERNANDO SANPORD. [^wS 

this equation. The equation Ve = hv has frequently been tested by 
experiment, but the assumption that all the energy given to an electron 
in an electrostatic field appears in the form of kinetic energy of the elec- 
tron has not been so tested. Whatever evidence may be derived from 
the relations here shown indicates that in this form h does not represent 
an energy quantum, but only a function of the mass of the electron. 



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Na'-J^^'] RESIDUAL IONIZATION IN A GAS, 349 



A STUDY OF THE RESIDUAL IONIZATION IN A GAS WITH 
REFERENCE TO TEMPERATURE EFFECTS. 

By C. H. Kunsman. 

Synopsis. 

A Siudy of the Residual lonitation in a Gas wUh Reference to Temperature Effects, 
— ^A form of electrometer was constructed which used the principle of the Wulf elec- 
trometer in separating the conduction of charge across the insulation from the 
conduction in the gas due to ionization. The new features of this apparatus were that 
it was possible (i) to make a quick and accurate test of the insulation properties 
under the same conditions as those under which the ionization tests were made, 
and (3) to subject the instrument to a wide range of temperatures. 

Ions generated per C.C. per Second.— The data experimentally determined show 
that the number of ions generated per c.c. per second within an air tight chamber 
is 8.22 in the basement of the Physical Laboratory and 4.15 over the Pacific Ocean. 

Residual lonitation not due to Thermal Impact. — The results of tests between 

— 44.6® C. and 92.5° C. show no indications that the residual ionization is due in 
any part to a molecular impact of thermal agitation. 

Effea of Temperature on Insulation System.^Obeeryationa made of changes in 
temperature on the insulation system, would seem to account for the apparent daily 
and seasonal variations of the residual ionization as previously reported. 

Conclusions from Observations at Low Temperatures. — ^At temperatures from 

— 30.5® C. to — 44.6® C. an increase in conduction across the insulation system 
was noticed, which was comparable to the apparent increase in ionization as reported 
at high altitudes. It would therefore seem that it is not necessary to assume, 
as has been done by previous observers, that there is a highly radioactive cosmic 
lajrer in the upper atmosphere; or that the sun is a source of penetrating radiation 
sufficient to generate 90 ions per c.c. per second. 

I. Introduction. 

THE experiments described in this paper were undertaken with the 
purpose of studying the ionization of a gas as observed in an air- 
tight vessel. This was done with a twofold purpose: (i) to find an 
accurate method of measuring this conductivity in the gas, and (2) to 
make a thorough investigation of the effect of temperature on this 
conductivity. 

C. T. R. Wilson^ and GeiteP were the first to notice that gases in 
closed vessels conducted electricity and were therefore ionized. The 
more recent experiments of Simpson and Wright,' King,* Murray,^ 

1 Wilson, Proc. Camb. Phil. Soc., II., 52, 1900. 

*Geitel, Phys. Zeit., a, 116, 1900. 

•Simpson and Wright, Roy. Soc. Lon. Proc., 85, 175, 1911. 

* King, Phil. Mag., 26, 610, 1913. 

^ McLennan and Murray, Phil. Mag., 30. 430, 19 15. 



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350 C. H. KUNSMAN. g^'J 

McLeod,^ McLennan,* Wright,' and the author^ showed conclusively 
that ions are being generated in an airtight metal chamber, as free from 
radio-active substances as possible, at the rate of from 8 to 9 ions on 
land, and over the ocean and large lakes from 4 to 5 ions per c.c. per 
second. These results include observations made over practically every 
continent and ocean. Some observations indicate a pronounced varia- 
tion. Lassalle* notices a diurnal variation in the Philippine Islands, 
while Gockel* finds the value for the winter months of December and 
January lower by i to ij ions per c.c. per second than for the months 
of June and July. 

In connection with the ionization within a closed chamber, we are 
confronted with two problems: (i) to find the source of the residual 
ionization of from 4 to 5 ions which is obtainable when the chamber is 
screened naturally over large bodies of water, or artificially on land; 
(2) to find an explanation for the very large increase "in the ionization 
at high altitudes, as observed in a balloon by Hess^ and Kolhorster.* 
The latter reports an increase of from 4.3 ions at 2,000 meters to 80.4 
ions at 9,000 meters, over the values obtained at the earth's surface. 
Treleaven* concludes that the residual ionization of 4 ions is due to a, j8, 
and possibly 7 radiation emitted from the walls of the chamber. Murray^ 
comes to the same conclusion from observations of this effect when the 
walls of the chamber were of ice. Kingdon*® shows that a part of the 
residual ionization is due to thermal agitation and derives a formula 
which agrees with his experimental results. 

The only other experimental works are those of Patterson" and 
Devik." Patterson used a large iron chamber containing an electrode 
insulated by ebonite, and measured the current with an electrometer. 
He got a value of 61 ions, so it would be doubtful if he could observe a 
small temperature effect at ordinary temperatures. Devik attempted 
to measure the current at the instant of greatest compression in an 
adiabatic compression and found no effect at ordinary temperatures. 

» McLennan and McLeod, Phil. Mag., Oct., 740, 1913. 
> McLennan, Phys. Rev., 26, 526, 1908. 
•Wright. Phil. Mag., 17, 295. 1909. 

* Kunsman, Phys. Rev., 6, 493, 1915. 

* Lassalle. Phys. Rev., 5, 135, 1915. 
« Gockel, Phys. Zeit., 16. 350, 1915. 
' Hess, Phys. Zeit., 14. 610, 1913. 

« (a) Kolkorster. Phys. Zeit.. 14, 1153, 1914; (6) Ber. Deut. Phys. Ges., 13, 721, 1914. 

* Treleaven, Phil. Mag., 30, 427, 1915. 
10 Kingdon, Phil. Mag., 32, 397, 1916. 
" Patterson, Phil. Mag., 6, 231, 1903. 

" Devik, Sitz. d. Heid. Akad. Wiss., 24, 1914. 



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Vol. XVLl 
No. 4. J 



RESIDUAL IONIZATION IN A CAS. 



351 



The question has been theoretically investigated by Langevin and Rey/ 
and by Wolfke.« 

Results obtained by the author seem to throw light on each of the 
following questions: (i) Do molecules of gases under ordinary tem- 
peratures collide in such a way as to produce ionization? (2) Is it neces- 
sary to assume a source of ionization in the upper atmosphere sufficient 
to produce ions at the rate of about 90 per c.c. per second? 



II. Apparatus. 

Preliminary experiments on the measurements of the natural ionization 
at the State College of Pennsylvania, at the University of California,' 
and on the Pacific Ocean between San Francisco and Los Angeles, were 
made with a Spindler and Hoyer^® aluminum leaf electroscope designed 
for radioactive tests when the gases tested could be drawn into the 
ionization chamber. Two cham- 
bers of different sizes were essen- 
tial for the method used. 

More extensive tests were 
made by means of an electrome- 
ter designed by the author which 
could be subjected to a wide 
range of temperature. The ob- 
ject of this was to make it pos- 
sible to measure ionization down 
to the temperature of liquid air. 
The main feature of the instru- 
ment was that it provided an 
easy test for leak across the in- 
sulation system without altering 
the conditions under which the 
tests were made. Such a test of 
conduction over the insulation 
could not be made on the appa- 
ratus used by the observers pre- 
viously mentioned. 

Practically the entire apparatus was built of as pure zinc as obtain- 
able, since this metal seems more free from radioactive impurities than 
others. The ionization chamber A consisted of a zinc cylinder about 
20 cm. long and 10 cm. in diameter. Fig. i, the walls of the cylinder 




Fig. 1. 



* Langevin and Rey, Le Radium, lo, 142, 

* Wolfke, Le Radium, 10, 265, 1913. 



1913. 



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352 C. H. KUNSMAN. l^SSk 

being 2 J mm. thick. Into this screwed the upper part which consisted 
of a zinc box 5, forming the walls of the electrometer. The sulphur 
plug 5 holds in place the zinc electrode E, and another zinc rod K, upon 
which the aluminum leaf L was attached. A very small rod C moves 
up or down through the center of the zinc rod K, The rod C is raised 
or lowered by an insulated rod D which passes through a ground glass 
joint attached to the electroscope case. The volume of ^ or 5 can thus 
be electrically connected or separated as desired. The electric charge 
is communicated to the insulated system by means of the same rod D. 
After the system is charged, rod D is disengaged from rod C and grounded, 
as is also the case of the electrometer. An external dial on the case and 
an indicator on the charging rod assure the rod D being turned to the 
same position after each time the instrument is charged. 

The sulphur insulation was kept cool or warm as was necessary by 
means of a system Xi through which water or alcohol was run. A 
similar cooling system X2 kept the wax joints cool. 

Chamber B was kept as dry as possible by means of metallic sodium, 
contained in a receiver H. Thermo-couples Ti and Tt made it possible 
to measure the temperature of the gas quickly and accurately. A 
stopcock M permitted the ionization chamber to be exhausted and filled 
with dry gas. A spirit level V made it possible to keep the instrument 
always in the same position. A very fine quartz fiber was attached to 
the end of the leaf and the position of the fiber observed through windows 
by means of a telescope. The quartz fiber greatly increased the accuracy 
of the observations. 

The zinc electrode E could be easily removed and a small cup con- 
taining sodium could be sealed to the bottom of the water jacket iV, so 
that the loss of charge due to the volume B together with the total 
leakage across the insulation support could be determined. The volume 
of chamber A was 1,277 c.c. The electrostatic capacity of the elec- 
trometer as determined with two spheres of different radii,^ was 4.48 
cm. with the cup at N in place, and 6.50 cm. with the cup removed and 
the central electrode replaced. The drop in potential for a given number 
of scale divisions was obtained from the calibration curve, Fig. 2. 

III. Theory. 

If C is the electrostatic capacity of a body, which is charged to a 

potential £, and after a certain time some of the charge has disappeared, 

it is evident that we can express this loss, or change of quantity, of 

electricity as AQ = CAE; where AE is the drop in potential for a unit of 

» Lichtenecker» Phys. Zeit., 13, 516, 1913. 



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No!'4?^^H RESIDUAL IONIZATION IN A GAS. 353 

time At. This loss of charge may be thought of as a neutralization of N 
ions, each carrying the unit charge, e. If n is the number of ions formed 
per c.c. per second in the volume V in the time A/, we may write N=n VAt. 
It follows that AQ = CAE = iV£ = nAUV, or » = CAEjVeAt. 

Now A£ is made up of two parts (-4) a conduction of charge across 
the insulation support and (5) a loss of charge due to ions being formed 
in the gas, which neutralizes some of the charge on the insulated system. 
If two different volumes of gas are taken in such a way as not to alter 
the conduction of charge over the support, two equations can be set up 
of the form, Qi ^ A + BVx and Oi = ^ + -BFj; where Qi and Qt are 
the loss of charge per second with volumes Vx and Vt respectively and 
where B = ne. From this we get 

_ CiAE- CiAE 

"*" {Vx-Vt)e ' 

which is the formula used for all calculations of ». 

IV. First Investigation. 

In the first set of experiments dry, dust-free air was introduced in the 
ionization chamber of the Spindler and Hoyer electroscope, in which 
the amber insulation was replaced by sulphur. Observations were taken 
of the rate of fall of the leaf, or loss of charge, after the rate of loss 
became constant. An apparent soaking in of the electric charge was 
shown by the relatively rapid fall just after the instrument was charged. 
This effect lasted about two hours. Quite a pronounced increase in 
ionization was always noticed immediately after the instrument was 
filled with air. This effect largely disappeared in about 4 days, which 
leads one to conclude that it was due to radium emanation, its half 
period being 3.8 days. The rate of fall was observed for about 4 weeks 
for each ionization chamber, and a mean value of n calculated. The 
mean value of n as obtained in the basement of the physical laboratory 
was 8.68 ions. Variations in this number were observed. In the light 
of recent experiments, these variations can be attributed to a change 
in the temperature of the instrument and were not due to a change in 
ionization. 

In a test made the same year (1915) with the same apparatus, the 
value of n on the Pacific Ocean, between San Francisco, and Los Angeles 
was found to be 4.15 ions. In the calculation of the results of the 
observations over the ocean, the leak over the support was calculated 
from data obtained on land. The differences between the observed loss 
of charge on the ocean, and the calculated leakage across the support, 
as observed on land, was attributed to the formation of ions. 



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354 



C. K. HUNSMAN. 



rSscoiffD 
LSkriss. 



V. Second Investigation. 
The zinc electrometer was used in all experiments where the tempera- 
ture of the gas was varied. The instrument was made airtight by cover- 
ing all possible sources of leak with sealing wax and finally applying^ a 
number of coats of shellac. The ionization chamber was filled with air 
or carbon dioxide which was made as free from moisture as possible by- 
drawing the gas through calcium chloride and phosphorus pentoxide 
tubes, and finally bubbled through two bottles of concentrated sulphuric 
acid. The thermocouples, previously annealed and calibrated from the 
temperature of liquid air to the melting point of lead, were sealed into a 
hard rubber plug with sealing wax. This plug was. then screwed into 
the top wall of the ionization chamber, and covered with more sealing: 
wax. The other junctions of the thermo-couples were kept in a bath of 
melting ice. The E.M.F. was measured on a potentiometer in micro- 
volts. In practically all tests the instrument was charged in the even- 

Table I. 



Length 
of Test. 



Chamber v4 

Connected, 

Disconnected 

or Cnpfai Place. 



Arerage 
Temp, of 
Gas oc. 



Rate 

Scale 

Diw. 

perMfai, 



"I 



Rate 

Votts 

per Min. 



(Calculated). 



Remarks. 



Air. 



Udys. 


Conn. 


21to24*' 


.0915 


.02955 


8.22 


Instrument surrounded 
with felt. 


lOhrs. 


Conn. 


II II 


.0931 


.03007 


8.55 
(max.) 


Instrument surrounded 
with felt. 


8hrs. 


Conn. 


II II 


.0896 


.02914 


7.88 
(min.) 


Instrument surrounded 
with felt. 


Sdys. 


Cup in place 


II II 


.0703 


.02271 




Instrument surrounded 
with felt. 


10 dys. 


Disconn. 


II II 


.0336 


.01085 




Instrument surrounded 
with felt. 


20hrs. 


Conn. 


-12.5 


.0721 


.02603 


6.20 


Chamber immersed in 
ice and salt. 


lOhrs. 


Disconn. 


-12.5 


.0298 


.01076 




Chamber immersed in 
ice and salt. 


48 hrs. 


Conn. 


22.0 


.0815 


.02632 


6.37 


Chamber immersed in 
brine. 


Shrs. 


Disconn. 


22.0 


.0327 


.01056 




Chamber immersed in 
brine. 


5 hrs. 


Conn. 


34.0 


.0905 


.02920 


8.04 


Chamber in heater. 



Carbon Dioxide, 



7 dys. 
6 hrs. 



Conn. 
Conn. 



21to24*» 

38.8** 



.1104 
.0985 



.03566 
.03171 



11.95 
9.58 



Chamber in heater. 
Chamber in heater. 



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JJ*-^^^^] RESIDUAL IONIZATION IN A GAS, 355 

ing beyond the field of view of the telescope so that by morning it was 
within view. This did away with irregularities previously mentioned. 

The residual ionization was determined at room temperature for air 
and carbon dioxide. The results for carbon dioxide are somewhat higher 
than those obtained by Treleaven. Since commercial carbon dioxide was 
used the increase may be attributed to radioactive impurities in the gas. 
By means of the formula for n, the given constants of the apparatus and 
the data given in Table I., the resulting values of n were calculated. 

Tests were undertaken at low temperatures for two reasons: (i) if 
ionization is produced by molecular impact due to thermal agitation, 
such an effect could best be investigated by decreasing this molecular 
motion as much as possible, (2) there is no record of such tests being 
made at low temperatures. 

The electrometer was clamped rigidly in a frame and a Dewar flask 
containing solid carbon dioxide and alcohol raised until the ionization 
chamber was completely surrounded with the cooling solution. During 
this change of temperature of the gas within the chamber, very pro- 
nounced variations of the rate of leak were observed. When the warm 
instrument first came in contact with the cold solution, the divergence 
of the leaf increased a few scale divisions. However, in a few minutes 
the leaf came back to its original position, and quite a rapid rate of fall 
of the leaf was observed. For some time, depending upon how rapidly 
the temperature was lowered, the rate of leak appeared to be normal. 
With a further decrease in temperature the rate of loss of charge became 
quite rapid, and with a further lowering of temperatxu-e the charge on 
the insulated system had disappeared entirely. Table II. shows how 
this leak depends upon the temperature. 

The central electrode was then disconnected from the charged system 
and a similar set of results obtained, also given in Table II. This at 
once shows us that the increased conductivity takes place across the 
insulation. Repeated tests with additional precautions against air leaks 
were taken, and in every case the same effects were noticed. Separate 
insulation tests were made on sulphur, amber and hard rubber, in order 
to determine whether the increased conductivity at low temperatures 
was due to a property of the insulator or was due to the presence of 
water vapor. The insulators were attached to wires and were sealed 
into glass tubes. In some cases the tubes were exhausted and filled with 
air which had been passed through calcium chloride, phosphorous 
pentoxide, and concentrated sulphuric acid. No noticeable increase 
in the conduction was observed at the temperatures of — 72** and — 187** 
C, when the air was carefully dried. But in cases where water vapor 



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356 



C. H. KUNSMAN, 



rSBCONO 

ISbribs. 



Table II. 



Lensth of 


•^^^^^ 


Rate Scale 




Remarks. 


Obsemitioii. 


Temp, of 
GasoC. 


DiT. per 
MinV 


«.• 




aOmin. 


22.0 


.1010 


10.0 


In alcohol bath at room temperature. 


18 min. 


-30.5 


.1385 


20.0 


No warming bath used. 


50 min. 


-34.5 


.1310 


18.6 


No warming bath used. 


30 min. 


-29.0 


.1265 


' 17.6 


No warming bath used. 


40 min. 


-36.5 


.1250 


17.4 


No warming bath used. 


30 min. 


-41.0 


.1785 


28.8 


No warming bath used. 


10 min. 


-41.2 


.2778 


50.3 


No warming bath used. 


6 min. 


-43.2 


1.0820 


222.5 


No warming bath used. 


li min. 


-44.6 


5.4800 


1.162.0 


No warming bath used. 


} min. 


-44.6 


7.0500 


1.498.0 


No warming bath used. 


4 min. 








Small stream of alcohol used for warm- 
ing bath. 


7 min. 


-38.9 


1.0000 


204.0 


No warming bath used. 


2 min. 


-42.3 


4.1000 


867.0 


No warming bath used. 


6 min. 








Small stream of alcohol used for warm- 
ing bath. 


7 min. 


-38.8 


.8560 


181.5 


No warming bath used. 


10 min. 


-39.2 


.8550 


181.0 


No warming bath used. 


20 min. 


-40.1 


.6250 


124.5 


No warming bath used. 


25 min. 


-36.2 


.2320 


40.5 


No warming bath used. 

Air in Chamber-connected. 


Ihr. 


24.5 


.0938 


8.68 


No warming bath used. 


45 min. later 


-41.7 


charge lost 




No warming bath used. 


30 min. 


+20.0 


.1140 




Instrument recharged (25 min. later). 


8 min. 


-31.1 


.1250 


17.4 


Warming bath used. 


14 min. 


-31.1 


.1570 


25.1 


Warming bath used. 


11 min. 


-35.2 


.1820 


29.7 


Warming bath used. 


10 min. 


-33.4 


.2000 


33.4 


Warming bath used. 


11 min. 


-25.8 


.1630 


25.5 


Warming bath used. 


37 min. 


-28.1 


.162 




No warming bath. 


15 min. later 


-40.2 


charge lost 




No warming bath. 

Air in Chamber-disconnected. 


2hrs. 


22.5 


.0337 




Room temperature. 


45 min. 


-21.4 


.0248 




Warming bath used. 


36 min. 


-30.1 


.0694 




No warming bath used. 


20 min. 


-29.6 


.0588 




No warming bath used. 


8 min. 


-34.5 


.1250 




No warming bath used. 


5 min. 


-36.4 


.6450 




No warming bath used. 


1 min. 


-41.0 


3.2500 




No warming bath used. 




-41.0 


charge lost 




No warming bath used. 



* n calculated upon the supposition that the increased rate of loss of charge is due to 
ionization within the gas. 

was present an increased conduction took place. The rate of increase 
depended upon the insulator and form of the electrode. Insulation 
tests were also made above room temperature. Sulphur proved to be 



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Vol XVI. 
No. 4. 



] 



RESIDUAL IONIZATION IN A GAS. 



357 



the best insulator under all conditions. Amber seemed to be especially 
sensitive to traces of moisture. 

It was found that more even temperature conditions could be obtained 
at these low temperatures by allowing a small stream of alcohol at room 
temperature to flow through the system designed to keep the insulation 
cool when the gas was heated to higher temperatures. 

As seen from Table II., there is a very marked increase in conduction 
across the insulation support when the average temperature of the gas 
is from — 15"* C. to — 30"* C. and at a temperature of about — 41"* C. 
the charge is lost entirely. The temperature of the sulphur, although 
below zero, as shown by the amount of ice crystals which form on the 
external surface of the instrument, is not as low as the temperature of the 
gas, since the insulation part of the instrument is not immersed in the 
cooling solution. 

Kolhorter^* does not give the definite temperature of the electrometer 
for various altitudes, but states that when the temperature of the instru- 
ment had fallen to — 10® C. (5 to 6 km. above sea level) and below 
— 10® C. (6 to 9 km.) one would disturb the readings, if the electrometer 
was touched with the bare hands. In Table III., we have listed Kol- 
horster's results and probable atmospheric temperature for such eleva- 
tions. 

Table III. 



Elevation Zm^» Above 
SeaLerel. 


♦ Value in 19x3. 


*yahreinz9X4. 


tTemp.*C.» 



1 
2 
3 
4 
5 
6 
7 
8 
9 
10 






24.9 

21.6 

16.6 

10.3 

3.9 

" 2.5 

- 8.5 

-14.3 

-20.9 

-27.2 

-33.9 


- 1.5 
+ 1.2 
+ 4.0 
+ 8.3 
+ 16.5 
+28.7 






+ 4.3 
+ 9.3 
+17.2 
+28.7 
+44.2 
+61.3 
+80.4 













♦ Increase in ionization over value obtained on the earth's surface. 

t Mean value of atmospheric temperature based upon sounding balloon observations at 
Fort Omaha, Nebraska; Indianapolis, Indiana; Huron, South Dakota; and Avalon, Cali- 
fornia, for the summer season. 

^ Gregg, Month. Weather Rev., 46. 17, 1918. 

On comparing Tables II. and III. we see very marked evidence that we 
are dealing with similar results due most probably to the same cause, 
and that there are no abnormal ionization effects at great elevations; nor 



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358 C. H. KUNSMAN. [|;SS 

any additional source of penetrating radiation in that region. There is 
no need of introducing the theory of a very radioactive cosmic atmosphere 
at that elevation to explain these results. It also seems very improbable 
that the sun could be the source of a penetrating radiation sufficient to 
form 90 ions per c.c. per second within a closed vessel. And if the value 
of 90 ions represents the number generated at 9 km., might we not 
expect a much greater increase in ionization at 17 km. elevation where 
the temperature^ is about — 84® C? It does not seem at all unreason- 
able for us to believe that results would be obtained which would be in 
agreement with those in Table II. 

In order to get such large results by experiments with a radioactive 
substance, it was necessary to place a considerable quantity of a very 
active material quite close to the chamber. This would lead us to believe 
that it is very improbable that there would be such quantities of radio- 
active material in the upper atmosphere as it would require to produce 
ionization at this rate. Then again experiments on the earth's surface,* 
show that the radioactive content of the atmosphere only contributes 
from 0.1 to 0.2 ions per c.c. per second, to the residual ionization. It 
would thus be necessary for the upper atmosphere to be from 450 to 900 
times as radioactive as the atmosphere close to the earth's surface. 

There seems to be no record of insulation tests being made at these 
altitudes. The author has found in measurements made with a similar 
Wulf electrometer obtained from Germany, that there is a very probable 
air leak when the change from one volume to the other is made, and in 
order to keep the gas as dry as possible, it is necessary to replace the 
metallic sodium from time to time. It would seem that the moisture 
in the closed gas has no noticeable effect on the insulation at ordinary 
temperatures, but when sufficiently low temperatures are reached minute 
ice crystals form on the insulation and conduct the charge to the walls 
of the instrument; again when the enclosed air is sufficiently warm, 
these crystals vaporize and normal conditions are established. One 
notices (see Table II.) that at one instance the rate had increased to 7 
divisions per minute, and on allowing a small stream of alcohol at room 
temperature to flow through the water jacket for 4 minutes, the rate was 
decreased to one division per minute. A similar effect was noticed a 
little later in the test when a small stream of alcohol running 6 minutes 
caused the rate to change from 4.1 to 0.856 divisions per minute. No 
matter how rapidly the loss of charge takes place at low temperatures 
on bringing the temperature of the instrument back to room temperature 
the rate of loss of charge again becomes normal. 

1 Nature, 98, 21, 1916. 

' Chauveay, Le Radium, 10, 18 and 70. 1913. 



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No!"4.^^^*] RESIDUAL IONIZATION IN A GAS. 359 

Other observations were made with the instrument surrounded by a 
mixture of ice and salt (Table I.) in this case the temperature of the 
gas was subject to only small variations during the test. Since a pro- 
nounced decrease in the loss of charge was noticed, tests were made when 
the chamber was surrounded with the same brine at room temperature. 
Differences were observed both when the chamber was connected and dis- 
connected. A search for the difference led the author to calibrate the 
instrument at the corresponding temperatures. The result was two 
distinctly different calibration curves as given in Fig. 2. At room-tem- 
perature one scale division is equal to 
0.232 volts; while at a temperature 
below zero, one scale division is equal ^ 
to 0.361 volts. So that on reducing 5 
the respective scale divisions to volts | 
per minute (Table I.) the rate of i^ 
loss of charge is the same, when the ^ 
gas is at — 12.5® C. in the ice and 
salt solution, or when the gas is at 
room temperature and the ionization 
chamber is immersed in salt water, voxr# 

The difference between 8.22 ions at pig. 2. 

room-temperature (Table I.) and 6.37 

ions with the chamber immersed in salt water is due to the screening 
effect of the salt water. 

For investigations above room-temperature, the ionization chamber 
was placed in an electric heater formed by winding climax wire about a 
thin cylindrical sheet of asbestos, and packing this heating coil in mag- 
nesia. The heater was made just large enough to contain the ionization 
chamber. Both the sulphur insulation and the wax joints were kept cool 
by water jackets. From three fourths to two and one half amperes of 
current were passed through the heating coil. The results, as given in 
Table IV., show no increase with temperature below 92.5** C, but from 
95 to 100® C. a pronounced increase is noticed, which is again evident 
when the volume is disconnected, at from 101° C. to no® C. This 
shows an increased conduction across the insulation support, and is 
sufficient to account for the apparent increase in ionization in the gas 
noted by Kingdon from 80"* to 100° C. His only method of testing the 
insulation was to exhaust the chamber. Thus different conditions were 
introduced whenever the insulation tests were made. 

One notices from Table IV. that from 22° to 92.5° C. and from 22"* to 
101° C, with volumes connected and disconnected respectively, there 



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36o 



C. H, KUNSMAN. 

Table IV. 

Air above Room Temperature, 



Chamber Connected. 


Chamber Disconnected. 


Temp. « C. 


Scale Div. per Min. 


Chamber Temp. * C. 


Scale DiT. per Mfau 


22.5 


.091 


22.0 


.0333 


38.0 


.089 


54.0 


.0310 


43.0 


.088 


76.0 


.0308 


52.0 


.090 


90.5 


.0306 


56.0 


.087 


95.0 


.0300 


68.0 


.087 


101.0 


.0412 


82.0 


.079 


109.5 • 


.0450 


90.0 


.085 






92.5 


.091 






95.0 


.132 






100.0 


.130 







IS a decided decrease in the rate of loss in scale divisions per minute, in- 
stead of an increase as would be the case if there were an increase in the 
ionization. This change is no doubt largely due to a change in the 
dielectric constant of the sulphur. 

The effect of temperature upon the insulated system can be easily 
shown by allowing solutions of different temperatures to flow through the 
water-jacket surrounding the sulphur insulation. When water at room 
temperature is allowed to flow through there is no change in the position 
of the leaf. When a solution above room temperature passes through, 
the leaf at once took a higher position on the scale. When a cold solution 
was allowed to flow through the water-jacket the leaf immediately took 
a lower place on the scale than that which it occupied at room tempera- 
ture. When the temperature of the instrument was again at room 
temperature the leaf returned to its original position, except for the 
natural loss of charge which took place in the mean time. The greater 
part of this change is due to the change in the dielectric constant of the 
sulphur for various temperatures, as is shown by Schmidt.^ A small 
variation may also be due to the change in the flexibility of the aluminum 
leaf with the change in temperature. 

Bearing in mind that it requires a change of about 0.005 scale divisions 
per minute for an increase or decrease in the generation of one ion per 
c.c. per second, we find, on referring to Table I. and IV. that we cannot 
attribute the residual ionization to a thermal agitation of the molecules. 
Since the apparent variations in ionization can be attributed to tempera- 
ture effects on the insulation system, it does not seem reasonable to 

* Schmidt, Ann. der Physik; 44, 335, 1914. 



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Na'4-^^^*] RESIDUAL IONIZATION IN A GAS. 36 1 

attribute any part of the residual ionization to a temperature effect 

upon the gas. 

VI. Summary. 

1. The mean value of the electrical conductivity of air in the base* 
ment of the physical laboratory at the University of California was 8.22 
ions* per c.c. per second when measured in a zinc chamber and 8.68 ions 
per c.c. per second when measured in a chamber where part of the walls 
were brass and the other part aluminum. 

2. The mean value of the electrical conductivity as measured on the 
Pacific Ocean was 4.15 ions per c.c. per second. 

3. This electrical conductivity, or residual ionization, is not due to 
molecular impact of thermal agitation. 

4. The apparent increase in ionization as observed at high altitudes 
is solely a temperature effect, and is due to an increase in conduction 
over the insulation. 

5. The effect of changes in temperature on the insulation system of an 
apparatus of this kind is sufficient to account for the apparent daily 
and seasonal variations of the residual ionization as reported by some 
observers, and is not due to a variation of the ionization of the gas within 
the chamber. 

In conclusion I wish to express my thanks for the valuable guidance of 

Professor E. P. Lewis, under whose direction this work was done; and 

to Professor E. E. Hall for the laboratory facilities placed at my disposal, 

and also for helpful suggestions. Finally, acknowledgement is due Mr. 

W. R. Stamper for help in construction of apparatus. 

Physical Laboratory* 

University op California, 
March 31, 1920. 



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362 THE AMERICAN PHYSICAL SOCIETY. g] 



PROCEEDINGS 

OF THE 

American Physical Society. 

Minutes of the One Hundred and Fourth Meeting. 

A MEETING of the American Physical Society was held in- Denny Hall. 
University of Washington, Seattle, on June 18, at 9:30 o'clock in con- 
nection with a meeting of the Pacific Division, American Association for the 
Advancement of Science. About thirty members and visitors were in attendance. 

The following papers were presented: 

A Cable Loaded at One Point — A Special Case of the Catenary. S. H. 
Anderson. (By title.) 

The Gibbs Thermodynamical Model. W. P. Boynton. 

Transparency to Heat Radiation. S. L. Brown. 

Characteristics of Vaccum Tubes. S. L. Brown and C. F. Normand. 

A Study of the Residual Ionization in a Gas with Reference to Temperature 
effects. C. H. Kunsman. 

The Continuous Spectrum of Hydrogen in the Schumann Region. E. P. 
Lewis. 

Multiple Reflection from the Interior of a Ring. A. A. Knowlton and 
G. A. Watt. 

An Optical Illusion. A. A. Knowlton and G. A. Watt. 

Velocity of Sound from a Moving Source. R. B. Abbott and J. W. Cook. 

Voltage Wave Analysis with Indicating Instruments. Leslie F. Curtis.. 

The Dielectric Constant of Silk. F. J. Rogers. 

The Mathematical Structure of X-Ray Spectra. R. T. Birge. 

The Spectroscopic Committee of the Division of Physical Sciences of the 
National Research Council. C. E. St. John. 

Astronomers, mathematicians and physicists participated in a symposium 
on Einstein's Theory of Relativity June 17, at 2 o'clock, in Denny Hall. 
Dr. Eric T. Bell read a paper on the principle of general relativity, and there 
was a discussion led by Dr. J. H. Moore and Professor E. P. Lewis. 

The Spectra of Compound Gases Flowing in Vacuum Tubes. W. H. Bair. 

On Friday evening President Suzzalo and the Committee on Arrangements 
gave a dinner to members of the affiliated societies. 

E. P. Lewis, 
Local Secretary for the Pacific Coast. 



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NoV?^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 363 

A Catenary Loaded at One Point. 
By S. H. Anderson. 

A FLEXIBLE string, hung between two points at different horizontal 
levels and loaded at some point between the two supporting points, 
assumes a conformation with a point of discontinuity at the position of the 
load, which divides the string into two arcs. It may be shown that each of 
these arcs is a portion of a catenary. 

From a consideration of the forces acting upon one of these arcs a differential 
equation may be obtained the solution of which gives the two following 
equations: 

(y + yo)^- (e*'« + f-("^>) + - (e'f' - «-<*/<=>), (i) 

2 2 

(5 - 5) = ^ (e*'<' - «-<*'<=>) + - {e'f<^ + e-<*''>), (2) 

2 2 

in which x, y are the rectangular codrdinates of any point, P, s is the length of 
the arc between the loaded point and P, and yoi ^0, and c are constants or 
parameters of the curve which depend for their values upon the weight of the 
string and the load, and are connected by the following equation 



yo = V50* + c«. (3) 

The interpretation of the three constants is as follows: If the arc is extended 
to a point where the tangent becomes horizontal, sq is the length of this auxiliary 
arc from the point of loading to the point where the tangent is horizontal; c is 
the vertical distance from this latter point to a horizontal line which may be 
called the directrix; and yo is the vertical distance from the point of loading to 
the directrix. 

If in the above equations ^0 is put equal to zero, which will be the case when 
there is no load upon the string, (i) and (2) reduce to 

(y + c) =^(e«/^ + e-C*/c)), (5) 

5 = -{e"' - e-^"'^), (6) 

2 

which are the equations for the common catenary. This shows that the loaded 
catenary is a more general case of which the common catenary may be consid- 
ered a special case. 

The total tension at any point is given by 

T==wiy + yo). (7) 

The vertical component and the horizontal component are given by the follow- 
ing equations respectively: 

Tv = w(d + ^0), (8) 

Tg = wc, (9) 

in which w is the weight of unit length of the string. 



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364 THE AMERICAN PHYSICAL SOCIETY. ItoiS 

The equations for the other arc of the string are of the same form, but the 
parameters ya and 5o are different, and c the same. Hence in general the form 
of the curve will be different. Let us call these parameters yo' and 5o'. Then 
it may be shown that the load is given by 

W = w{so + So'). (10) 

This ideal case may be considered an approximation to the problem of the 
aerial tramway as is used in the logging "skyline'* for transporting logs out of 
the forest. The chief factor of the practical problem that is neglected in the 
above treatment is the stiffness of the cable. However the length is generelly 
very great as compared with the diameter so that the relative stiffness is very 
slight except at the ends where supported and at the carriage where the load 
is applied. 

Perhaps the most valuable feature of the above analysis is the determination 
of the factors necessary to compute the load a given cable will carry. They 
are as follows: (i) the horizontal distance between the end points of the cable; 
(2) the vertical distance between these points; (3) the length of the cable, or 
the position (with reference to one of the end points) of the lowest point in the 
sag of the cable that the topography of the ground will allow; and (4) the 
breaking strength of the cable. 
University of Washington. 

GiBBs Thermodynamical Models. 
By W. p. Boynton. 

GIBBS first suggested the representation of the thermodynamical properties 
of a substance by a three-dimensional model having for co6rdinates 
the volume, entropy and energy. Maxwell constructed such a model, and in 
his "Theory of Heat*' presented a diagram of the principal lines upon it. 
The writer has also constructed a model intended to represent the model 
described by Maxwell. Finding difficulty in coordinating its form and the loca- 
tion of the lines upon it with the known properties of substances, he computed 
these lines for a substance following van der Walls' equation, with the ratio of 
its specific heats i 2/7, and constructed a model from these graphs. Lately he 
has recomputed for a van der Waals* substance having the ratio of the specific 
heats I 2/3, the maximum value, and constructed a model to correspond, and 
has also constructed a model, modified to show the properties of the solid state 
also, which is not included in the van der VVaals' equation. These models must 
be at least qualitatively correct, and show in a general way what the surface 
must be like for an actual substance. 

The moulds for the models have been preserved so that more copies may 
readily be made. The writer has also drawings and lantern slides showing 
contours and projections of principal lines upon the planes, and the appearance 
of the finished models. 
University of Oregon, 
Eugene, Oregon, 
May, 1920. 



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Vol. XVI.I 
No. 4. J 



THE AMERICAN PHYSICAL SOCIETY. 



365 



Characteristics of Vacuum Tubes. 
By S. L. Brown and C. E. Normand. 

SEVERAL types of vacuum tubes for detection, amplication and generation 
of radio-frequency currents have been examined in order to compare 
types of tubes and different tubes of the same type. The different types of 
vacuum tubes examined include those from American, French and German 
manufacturers. 

Data Showing Characteristics of Vacuum Tubes at their Rated Filament Current 

AND Plate Voltage. 



Western Electric. VT i; filament current i.i amp., plate voltage 20 volts. 

General Electric, VT 11; filament current i.i amp., plate voltage 30 volts. 
Type III: General Electric, VT 14; filament current 1.4 amp., plate voltage 400 volts. 
Type IV: Marconi. Class I; filament current .6 amp., plate voltage 40 volts. 

French. Bis 3; filament current .6 amp., plate voltage 20 volts. 

German. EVN 117; filament current .6 amp., plate voltage 50 volts. 



Type I: 
Type II: 



TypeV: 
Type VI: 



Type. 


Grid Voltage. 


Plate Current. 


Type. 


Grid Voltage. 


Plate Current. 


I 


-10 V. 


00 ma. 


IV 


-20 V. 


00 ma. 


II 


00 


.75 




-10 


.05 


II 


10 


2.65 




00 


.50 


II 


20 


10.10 




10 


2.05 


II 


30 


12.00 




20 


2.15 


II 


40 


14.50 




30 


2.05 


II 


50 


15.00 




40 


2.00 


II 


-10 


00 


V 


-20 


00 


II 


00 


1.00 




-10 


00 


ti 


10 


2.05 




00 


.10 


II 


20 


4.10 




10 


1.50 


tt 


30 


6.00 




20 


3.55 


II 


40 


7.25 




30 


3.80 


II 


50 


7.15 




40 


3.80 


III 


-50 


00 




50 


3.70 


II 


-40 


.45 




60 


3.65 


II 


-30 


1.10 




70 


3.65 


II 


-20 


3.25 


VI 


-20 


00 


II 


-10. 


10.10 




-10 


.10 


II 


00 


12.55 




00 


.50 


II 


10 


12.80 




10 


1.00 


II 


20 


13.00 




20 


2.10 


II 


30 


13.10 




30 


3.55 


II 


40 


13.15 




40 


4.00 


II 


50 


13.20 




50 


4.10 


II 


60 


13.20 




60 


3.80 


II 


70 


13.20 




70 


3.40 



University of Texas. 



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366 THE AMERICAN PHYSICAL SOCIETY. ^SSf! 

Transparency to Total Heat Radiation. 
By S. L. Brown. 

THIS paper gives the results of measuring the. percentage of total radiation 
transmitted by glass, rock-salt, mica, celluloid and paraffin for tem- 
peratures of radiating source from 200® C. to 1200® C. This work was under- 
taken to determine the possibility of selecting pyrometer screens which would 
intercept a known fractional part of the total radiation at a particular temper- 
ature. Results show that the per cent, of total radiation transmitted by 
ordinary sodium glass increases from about 6 per cent, for 200" C. as the tem- 
perature of the source to about 60 per cent, when radiating source is at 1200" C. 
The transparency of mica increases from 7 per cent, to 40 per cent, when the 
temperature of the radiating source is increased from 400® C. to 1200" C. 
University of Texas. 

A Study of the Residual Ionization in a Gas with Reference to Tem- 
perature Effects. 

By C. H. Kunsman. 

INVESTIGATIONS were undertaken with the purpose of studying the 
ionization of a gas as observed in an airtight vessel. This was done with 
a twofold purpose: (i) to find an accurate method of measuring this conductivity 
in the gas, (2) to make a thorough investigation of the effect of temperature on 
this conductivity. A double ionization chamber one compartment containing 
the electroscope, made it possible to eliminate insulation losses by taking obser- 
vation with the compartments connected or with the electroscope chamber 
above. 

Tests were undertaken at low temperatures for two reasons: (i) if ionization 
is produced by molecular impact due to thermal agitation, such an effect could 
best be investigated by drecreasing this molecular motion as much as pos- 
sible, (2) there is no record of such tests being made at low temperatures. 
The electrometer was rigidly clamped in a frame and a Dewar flask containing 
solid carbon dioxide and alcohol raised until the ionization chamber was 
cpmpletely surrounded wish the cooling solution. During this change of 
temperature of the gas within the chamber, very pronounced variations of 
the position of the leaf was observed. For some time, depending upon how 
rapidly the temperature was lowered, the rate appeared to be normal. With a 
further decrease in temperature the rate of loss of charge became quite rapid, 
and with a further lowering of temperature the charge on the insulation system 
disappeared entirely. The ionization chamber was then disconnected from the 
charged system and a similar set of results obtained. This at once shows us 
that the increased conductivity takes place across the insulation and is not due 
to a variation in the ionization in the enclosed gas. 

Separate tests on various insulations including sulphur, indicate that the 
increased conductivity is due to traces of water vapor which have no notice- 



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No"^^^*] ^^^ AMERICAN PHYSICAL SOCIETY. 367 

able effect except at low temperatures. Sulphur proved to be the best 
insulator under all conditions and through a wide range of temperature. 

For investigations above room-temperature, the ionization chamber was 
placed in an electric heater. Both the sulphur insulation and the wax joints 
were kept cool by water jackets. No increase in conductivity was noticed 
until the temperature of the enclosed gas was between gs"* C. and 100® C, 
when a pronounced increase was noticed. This increase was again noticed 
when the ionization chamber was disconnected from the charged system at 
about the same temperature, which proves that the increased conductivity 
takes place across the insulation support and is not due to an increased con- 
ductivity in the gas. 

From these experiments we may conclude : 

1. The mean value of the electrical conductivity of air in the basement of 
the physical laboratory at the University of California was 8.22 ions per c.c 
per second. 

2. The mean value of the electrical conductivity as measured on the Pacific 
Ocean was 4.15 ions per c.c. per second. 

3. This electrical conductivity, or residual ionization, is not due to molecular 
impact of thermal agitation. 

4. The apparent increase in ionization as observed at high altitudes is 
solely a temperature effect, and is due to an increase in conduction over the 
insulation. 

5. The effect of change in temperature on the insulation system of an appar- 
atus of this kind is sufficient to account for the apparent daily and seasonal 
variations of the residual ionization as reported by some observers, and is not 
due to a variation of the ionization of the gas within the chamber. 

University of California, 
May, 1920. 

The Continuous Spectrum of Hydrogen in the Schumann Region. 

By E. p. Lewis. 

REFERENCES have frequently been made to a continuous spectrum of 
hydrogen associated with the spark discharge at high pressure or with 
vacuum tube discharges at low pressure, but the conditions most favorable to 
its appearance and its extent have not been discussed. Kayser rather takes it 
for grantedt hat an intense discharge through a small capillary is the most 
favorable condition, and Schniederjost used that method, with poor success, 
for giving a background for absorption spectra. The writer pointed out some 
years ago that this spectrum could be best produced by using a rather large 
end-on tube, say one cm. in diameter, with a simple discharge of small current 
density, at a pressure of five mm. or more, and that it was greatly weakened by 
the use of a condenser and spark gap.* This spectrum extended to the limit 
of transmission of the quartz system, its gradual weakening apparently being 
» Science, 41. 947. I9IS- 



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368 THE AMERICAN PHYSICAL SOCIETY. ^; 

determined rather by the increasing absorption of the quartz and the diminished 
sensitiveness of the photographic film than by failure of emission. There was 
no sign of resolution into lines, and it extended well into the visible region as 
well to in the opposite direction, although the superposition of the many-lined 
spectrum made it impossible to determine its exact limit. The writer has 
recently had constructed a fluorite vacuum spetrograph, which made it 
possible to extend observations into the Schumann region. As anticipated, it 
was found that the continuous spectrum extends with undiminished intensity 
well into this region. At a wave-length of about 1800 it begins rather 
suddenly to diminish in intensity, and disappears about 1750. Faint 
bands attributed by Schumann and by Lyman to carbon monoxide make 
observations in this region somewhat uncertain. A little below 1700 the 
line spectrum of hydrogen reappears, with no trace of a continuous back- 
ground. Lyman refers to an absorption band of unknown origin in this 
region, but the fact that the continuous spectrum does not reappear 
with the lines shows that the limit is not far from the point specified. There 
may be some theoretical interest attached to the fact that this continuous spec- 
trum completely fills the region between the Balmer series and the Schumann 
line spectrum, with no lines whatever superimposed on it. 

This continuous spectrum offers the best background yet obtained for the 
study of absorption spectra in the extreme ultra-violet. Its perfect uniformity 
and continuity makes it far superior to the aluminum spark under water. 
Good photographs of the absorption spectrum of benzol have been obtained 
with an exposure of fifteen minutes. The absorption appears to be complete 
beyond about 1900. 

Lyman makes a casual reference to a continuous spectrum, and Schumann 
used it in the study of absorption spectra, but neither appears to have investi- 
gated the most favorable conditions for its appearance. 

Helium and neon resemble hydrogen in giving continuous spectra far into 

the ultra-violet, which are not, however, so intense as that of hydrogen. The 

continuous spectra given by parts of some nebulae may be due to hydrogen and 

helium. 

University op California, 
May. 1920. 

Multiple Reflections prom the Interior of a Ring. 
By a. a. Knowlton and G. A. Watt. 

LIGHT from a point source reflected at a concave cylindrical mirror of 
large aperture gives rise to the well known caustic. If the reflecting 
surface forms a complete ring multiple reflections occur which produce caustics 
of higher orders. Slides prepared from photographs showing these curves 
for the second and third order were shown. The equation for the nth caustic 
has been obtained by a simpler method than that used by Cayley, who treated 
the theory of such reflections. 
Rbbd College. 
May, 1920. 



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NaV^^^'] ^^^ AMERICAN PHYSICAL SOCIETY, 369 

An Optical Illusion. 
By a. a. Knowlton and G. A. Watt. 

IF one stands with his back toward a window and looks into an ordinary 
flask nearly filled with clear water and held slightly above the level of his 
eyes he appears to see, near the bottom of the flask a bubble of oil or other 
highly refractive substance. This is in fact an image of the plane surface of 
the water distorted by reflection in the spherical mirror of large aperture and 
by refraction. Examples of this phenomena were shown and the cause of the 
illusion discussed. 
Rbbd College, 
May, 1920. 

Velocity of Sound from a Moving Source. 
By R. B. Abbott and J. W. Cook. 

OBSERVATIONS have been made which do not show any change in the 
velocity of sound due to a spark source moving 83^0 cm, per second. 
The source consisted of a spark gap mounted on the end of a vane rotating 30 
R.P.S. The spark was made to occur at the same point once in a revolution. 
Opposite points on the spherical wave front were located by two telephone 
transmitters and one receiver connected to a diff^erential transformer. A 
minimum sound in the receiver indicated that the wave front arrived at the 
two transmitters, simultaneously. The radii of the spherical waves measured 
varied from 190 to 260 centimeters. Normal room temperature and pressure 
prevailed. 

The conclusions are that the velocities of sound disturbances produced by a 
moving spark are not appreciable aff^ected by the velocity of the gap. 

Whatever increment of velocity may have been given to the sound by the 
motion of the gap, was damped out too quickly to affect the measurements 
beyond the errors involved. 
University of California, 
May 25, 1920. 

Voltage Wave Analysis with Indicating Instruments. 
By Leslie F. Curtis. 

AN investigation and instrument are described which were inspired by the 
lack of a suitable workable standard of wave form. The use of telephone 
condensers, air core inductances, and a sensitive hot-wire galvanometer to 
determine the order and amplitude of the harmonic components of a wave — 
leaving only their phase positions undetermined — is described. The method 
of analysis is based on the well-known use of the wave meter, but adapted to 
low frequencies and with this important difference — a fundamental frequency 
is always present, may not be neglected, and must be treated simultaneously 



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370 THE AMERICAN PHYSICAL SOCIETY. ^^SSSS. 

with the other harmonics. The equations used are developed and explained 
under the headings "Order** and "Amplitude** of the Harmonics. The 
sensitiveness of indication is discussed and applied to several types of circuits. 
A convenient arrangement of the constants of the circuit in an instrument 
called by the author an "Harmonimeter** and giving direct readings of the 
order of the harmonics and easily calculated values of their amplitude is illus- 
trated. An example of wave form measurement is given in which the results 
are checked by oscillogram. 

UNrvERsmr op Washington, 
Seattle, Wash. 

The Dielectric Constant of Silk. 
By F. J. Rogers. 

SILK does not appear in any of the usual tables of dielectric constants, 
probably no such measurements have ever been made. 

In general, when two dielectrics are electrified by contact and friction, the 
one having the larger constant becomes positive. If this holds true with silk 
and other substances then its dielectric constant must be rather large. This 
is what suggested the measurement of this constant for silk. 

The usual condenser method was adopted. As a silk fabric is not a contin- 
uous solid, some method must be used which will allow for the space between 
the condenser plates which is not filled with silk. This was done in two ways. 
First, several thicknesses of silk were used and the thickness measured while 
weighted between the condenser plates. The ratio of silk to air was then 
computed from the weight of the silk, the total volume, and the density of 
the silk. The density of the silk was determined by the simple expedient of 
weighing it in air and in water. The density proved to be surprisingly large, but 
as the silk fibers are solid and of a horny nature this ought to have been expected. 
In the second method the silk was dipped in melted paraffin and the "paraf- 
fined** silk used between the condenser plates. In this case to insure contact 
the lower plate was amalgamated zinc with a large excess of mercury and the 
upper plate was liquid mercury. In both cases it was assumed that the dielec- 
tric contact of the mixed dielectric was a simple additive function of the two 
dielectric constants for silk and air and for silk and paraffin. 

The simple bridge method was used for measuring the capacity of the con- 
denser having silk as a dielectric. It formed part of one of the condenser 
arms of the bridge and its capacity was determined by the substitution of 
variable calibrated air condenser. Alternating E.M.F. of 60 cycles was sup- 
plied to the bridge, and a quadrant electrometer was used as an indicating 
instrument. The electrometer needle was maintained at a high alternating 
E.M.F. of the same frequency and in quadrature with that supplied to the 
bridge. 

The experimental results obtained were as follows: 



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Voc XVI.1 
No. 4. J 



THE AMERICAN PHYSICAL SOCIETY. 



37' 





Specimen. 




White Sfttin. 


Black Satin. 


White SiUc. 


Density 


1.51 
4.62 
4.68 
4.58 


1.515 
5.07 
5.07 
4.86 






4.62 


Silk and air exp 


4.68 


Dielectric constant 


4.58 


Silk and paraffin exp 













Stanford University, 
May, 1920. 

The Mathematical Structure of X-ray Spectra. 
By R. T. Birgb. 

THE mathematical relations of X-ray spectra may be divided into two 
classes, (i) those concerning the same spectral line as it appears in the 
spectra of successive elements (Moseley's yjp : N curves) and (2) those con- 
cerning the various lines of any one element. Using the very accurate data 
now available, the author has tested many of the previously proposed relations, 
as well as some new ones. The work is still in progress. 

Under (i), the Siegbahn 19 19 data for nine Ka% lines, extending from N = 
17 to iV = 29, plus that for N = 74, have been fitted to an ordinary power 
series equation. A fourth degree equation (five undetermined constants) 
was found entirely satisfactory, the average 0-C values being 1/300 per cent., 
with no evidence of systematic divergence. The agreement for the smaller 
atomic numbers is especially good, and so the extrapolation to hydrogen and 
helium can be made with some confidence. The value for iV = i is 2535 A., 
with a possible error of not more than a few hundred A. (Uhler obtained 
400 A. or less.) The theoretical "resonance" line is 1216 A. For helium the 

o • 

extrapolated value is 470.7 A., — the resonance line 567 A. Theoretical con- 
siderations indicate that H and He have no Kai line, and so the disagreement 
is to be expected. The author's curve has an intercept N = + 0.23. 

The general equation of the second degree (a special form of which was used 
by Uhler) was found unsatisfactory. Duane has proposed a linear relation 
between velocity and atomic number, for K critical absorption, but his formula 
for kinetic energy, from which the velocity was obtained, is incorrect, and 
therefore the results must be considered purely empirical. 

It is noteworthy that the ^|v : N curves are smooth, even for the lowest 
atomic numbers, and that each curve seems to begin when there are only two 
electrons in the ring (or shell) from which the emitting electron comes. None 
of the graphs are linear, although in some cases the slope varies only about 
10 per cent., — in others 40 per cent, to 50 per cent. 

The only satisfactory relations, under the second type of regularity, are 
given by Sommerfeld in a chart. ^ Even these are only partially satisfactory 

* Zeitschrift fOr Physik, Vol. i. page 137, 1920. 



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372 THE AMERICAN PHYSICAL SOCIETY, ^S^ 

since Kai + Lai + Mai + Nai + etc. does not equal K absorption. In 
fact, it would be necessary to change all Stenstrom's M series data (both 
emission and absorption) by about 15 per cent., in order to obtain a general 
agreement. The combination principle appears strictly accurate in certain 
restricted types of relations, but quite inaccurate in general. 

The fact that certain -yjv : N curves of the L series cross one another proves 
that there must be various independent configurations of the atom. Thus far, 
in the theoretical X-ray work, only one set of related orbits has been considered. 
For ordinary spectral series there are four such sets of orbits (fundamental, 
principal, sharp, and diffuse.) 

D. L. Webster's relations between emission lines and critical absorption are 
extremely significant, but the fact that the Lt critical absorption curve* crosses 
the 72 emission curve, raises a vital objection, on quantum theory, to the 
association of 72 with Lt absorption. There are other similar cases. 

Overn*s eight equal frequency ratios for Tungsten are interesting, but 
unfortunately only two (fii/ai and 71//81) can be tested for other elements. 
The two ratios are not equal except for Tungsten, the curves (ratio against N) 
crossing at N = 74. Can it be possible that all eight curves will be found to 
cross at the same point? Additional experimental data is much to be desired. 
Univbrsity op California. 

The Spectroscopic Committee of the Division of Physical Sciences 
OF the National Research Council. 

By Charles E. St. John. 

IT is not necessary to recall to this body the part played by the Nationals 
Research Council in organizing the scientific resources of the country for 
the purpose of winning the great war. It was, however, a revelation to the 
country as a whole of the strength and weakness of the pre-war conditions in 
scientific work. The great success with which men trained in pure science 
attacked the various practical problems of the war increased the estimation 
in which scientific research was held and has made it possible to carry on under 
peace conditions some of the benefits of organization and to increase the foster- 
ing agencies of research in pure science. In line with such considerations and 
the executive orders issued by the President outlining the purposes of the 
Council, the National Academy reorganized and put upon a permanent basis 
the National Research Council whose purpose is " to promote research in mathe- 
matical, physical, and biological sciences, and in the application of these 
sciences to engineering, agriculture, medicine, and other useful arts, with the 
object of increasing knowledge, of strengthening the national defense and of 
contributing in other ways to the public welfare." In paragraph 3 of the 
order issued by the President an important point is expressed as follows: 
*'to promote cooperation in research, at home and abroad, in order to secure 
concentration of effort, minimize duplication, and stimulate progress; but in all 
1 Duane's 1920 data, not yet published. 



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Na"4?^^'] ^^^ AMERICAN PHYSICAL SOCIETY. 373 

co6perative undertakings to give encouragement to individual initiative as 
fundamental to the advancement of science." 

In furtherance of the purposes of the Council the Division of Physical 
Sciences, among others, has been organized of which Dr. C. E. Mendenhall is 
chairman. Other members of the Division are representatives of the related 
societies. In accordance with the provisions of the Council, the Division 
of Physical Sciences has recently established a General Spectroscopic Committee 
of ten members divided into an Eastern and a Western group. Before enter- 
ing into the committee's plans in detail it may be of interest to refer to the 
financial situation. 

The Rockerfeller Foundation has entrusted the Council with the expenditure 
of $500,000 within a period of five years for providing fundamental research in 
physics and chemistry, primarily in educational institutions of the United 
States. This purpose is to be carried out through establishing a system of 
fellowships to be awarded to American citizens whose training is equivalent 
to that represented by the doctor's degree. 

Important results are hoped from this undertaking and such a degree of 
success in accomplishing the ends in view that conditions in American centers 
of research will be permanently improved. Some of the results expected are: 

1. Opening of a scientific career to a larger number of investigators and 
their more thorough training in research, thus meeting an urgent need of our 
Universities and industries. 

2. Increase of knowledge relating to the fundamental principles of physics 
and chemistry. 

3. Creation of more favorable conditions for research in this country. 

In addition to the fellowship funds placed at the disposal of the Division of 
Physical Sciences, the Rockerfeller Foundation has also appropriated funds to 
meet the expenses involved in conferences of special committees and in the 
honoraria of investigators to whom the preparation of special reports, surveys. 
or monographs is committed. In fact the funds necessary to set the mach- 
inery in action are provided and it now remains to be seen how men of science, 
young and old, rise to the opportunities. It may well be that the next few, 
years will be crucial ones in developing physical science in the United States 
and it behooves us all to aid in all ways we are able, either by joining in or 
promoting interests in research, by preparing others for it, or by helping to 
create an understanding and hence a sympathetic attitude on the part of the 
general public toward increase in our knowledge of the fundamental facts and 
principles of physics, irrespective of their immediate practical applications. 

The Eastern group of the Spectroscopic Committee consists at present of 
Lyman, Chairman, Gale, Randall, Saunders, and Uhler, the Western Group of 
Anderson, Babcock, King, Lewis, and St. John. 

The activities of the committees are as yet but partly organized, but they 
hope so serve as clearinghouses of information as the means of correlating the 
work so that needless duplication may be avoided, and of bringing into closer 
relations men who are working along similar lines in different parts of the 



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374 ^^^ AMERICAN PHYSICAL SOCIETY, [MSS! 

country. It is already evident that men are going to appreciate the contacts 
with the outside which the committees supply, and that the committees will 
be able to render assistance in approaching the administrators especially of 
our state universities in the interests of fundamental research, helping to create 
a more favorable atmosphere and to bring about a more generous provision 
for research. 

At present a canvass of the universities is under way to ascertain the equip- 
ment and opportunities available and the lines of investigation in progress. 
Such a body of data will be of great service to the committee when responding 
to requests for suggestions as to lines of investigation that will fit into general 
plans or that need to be undertaken. 

It is expected that subcommittees, membership not confined to the main 
committee, will soon be organized for discussion and report on special fields 
which are best suited for or are in need of such a survey. The consideration 
in view would be as follows: 

1. They would be stimulating and valuable to the men themselves. 

2. The groups might undertake to interest others in their special fields. 

3. The reports would be of value to all physicists in helping them to get into 
touch with various phases of spectroscopic work. 

Correlated with the work of the general committee is that of the International 
Commission for Standards of wave-length. The American Committee re- 
porting at the Washington meeting preliminary to the Brussells conference 
was unanimous in the opinion that one of the greatest needs of the physicist at 
the present time is a complete determination of the wave-lengths of the elements 
with the utmost accuracy possible. Such an undertaking will require the 
united work of many investigators but its value will be commensurate to the 
cost in time and effort. It is well suited to cooperative efforts, as each in- 
vestigator or small group of investigators can have a definite field and feel 
the satisfaction that he is contributing an element of value to the larger work. 
Experience has shown that such investigations, besides accomplishing the im- 
portant ends directly in view, can hardly fail to yield valuable results in 
related fields, in particular in connection with problems of radiation, and in 
the relations between spectra of terrestrial and cosmic sources. 

There is much said of correlation and cooperation but it must ever be borne 
in mind that the greatest asset in research is individual initiative and that 
in all our efforts at cooperation the aim should be to discover and recognize 
early the fortunate possessor of this rare and prescious gift and the utmost 
care be taken that in our desire for efficiency of organization the machinery 
does not hinder its free and full development. 
Mt. Wn.soN Observatory. 



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Second Series November, igzo Vol. XVI., No. 5 



THE 

PHYSICAL REVIEW. 



ARCING VOLTAGES IN MERCURY VAPOR AS A FUNCTION 
OF THE TEMPERATURE OF THE CATHODE. 

By T. C. Hbbb. 

Synopsis. 

Low Voltage Arcs in Mercury Vapor.^-One of the objects of this work was to 
study the production of the low-voltage arcs in a more uniform mercury-vapor 
atmosphere than had been used before. As a result of improved apparatus much 
more consistent results have been obtained. It has been shown that there is a 
linear relation between the striking voltage and the current through the cathode 
for the larger currents. This in turn has been shown, in the case of platinum 
coated with lime, to mean that the striking voltage forms a linear relation with the 
temperature of the cathode. The results further suggest that the difference between 
the potential at which ionization takes place and the accepted ionization potential 
is directly proportional to the absolute temperature. Results with Tungsten Cath- 
odes, — In line with the above it has been shown that tungsten cathodes produce 
lower arcs than lime-coated platinum cathodes. A striking voltage as low as 
3.2 volts was obtained, the lowest for platinum coated with CaO having been in 
the vicinity of 4.9 volts. Effect of Thickness of Oxide Deposit on the Cathode, — It 
has been shown that the thickness has an effect on the value of the striking voltage. 
A thinly coated platinum cathode produced an arc at a potential as low as 6.0 
volts whereas a thickly coated one produced an arc as low as 4.9 volts. Effect of 
Hot Anode, — A hot anode used with a thinly coated platinum cathode has been 
found to produce a lower arc than when the anode was not heated. Discussion of 
Results, — The results are briefly discussed but no definite theory is offered to explain 
them. 

IN two previous papers^ I have shown that mercury vapor can be 
ionized at potentials as low as about 5 volts. These results which 
were somewhat contradictory to those of McLennan and Henderson' 
have since been substantiated by McLennan.* As the type of apparatus 
used in my previous experiments was considered unsatisfactory for the 
better understanding of the relations between the various factors involved 

» Phys. Rbv.. Vol. 9, p. 686. 1916. and Vol. 11, p. 170, 1918. 
«Proc. Roy. Soc., A, Vol. 91, 191S. 
» Proc. Phy. Soc. Lon., Vol. 31, Dec, 1918. 

."^75 



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376 r. c. HEBB, 

in the production of the low ionization, I have constructed and used 
the following apparatus. 

The glass tube A, Fig. i, about 2.5 cm. in diameter, was cemented 
with Khotinsky cement to the base BB which stood on the shelf 55. 
Through the plug P three holes were bored — one to admit the barometer 
tube / and the other two to admit two electrodes for conveying the 
current to the cathode c. The anode, a, was attached to an aluminum 
cylinder which was inserted in the side tube m. Electrical connection 
was made between the anode and the mercury in the tube jR by a platinum 
wire which passed down the tube U, The apparatus could be evacuated 
through the tube U as indicated in the figure. The upper part of the 
apparatus was surrounded by an asbestos furnace containing a glass 
window. The furnace was heated electrically. By the use of this 
apparatus a uniform mercury-vapor atmosphere could be obtained 
around the anode and cathode. The pressure of this vapor could be 

obtained by raising the reservoir Y until 
the mercury stood in the tube U. The ap- 
^ paratus was evacuated by means of a Toep- 

ler pump and the pressure of the j-emaining 
gas was measured with a McLeod gauge. 
During the process of *' heating up" of the 
apparatus and of the cathode a great deal 
of gas was given off. Pumping was con- 
tinued, however, until the pressure was of 
the order of .001 cm. In order to obviate 
^^^^^^^^^ the collection of this gas in the apparatus 
i4, the mercury in R was not allowed to 
shut off the tube U. As is evident, the 
evaporation of mercury in the tube A and 
its passage out through U rapidly clears 
the tube A of any foreign gases. The ther- 
mometer T had its bulb placed below the 
level of the surface of the mercury in A and very near the outside of 
the tube. 

The cathode, unless otherwise stated, w£is of platinum foil about 
.0025 cm. in thickness. Various widths were used but the length was 
about 2.0 cm. Either CaO or SrO was placed on it. The anode A was 
either platinum foil or platinum wire. 

It was soon found that much more consistent results could be obtained 
with this apparatus than with the previous type. With my earlier 
apparatus I found that it was necessary to have the pressure, as read 



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Na's^^^] ARCING VOLTAGES IN MERCURY VAPOR. 377 

by a McLeod gauge, at a particular value in order to get the lowest arcs 
and that a greater or less pressure increased the value of the arcing 
voltage. ' With the present form I found that the pressure of the mercury 
was of less importance. It still had to be above a certain minimum 
value but, aside from that, no great care had to be exercised. If the 
thermometer read anywhere between 170 and 220° C. the results were 
practically the same. This gave a vapor pressure of the order of 1-3 cm. 
of mercury. 

As in the previous work so here it was found that the electronic density 
was important. Low temperature cathodes would not give low arcs. 
As the temperature of the cathode rose, however, the striking voltage 
dropped rapidly until a further increase had only a small effect on the 
striking voltage. This is brought out by Fig. 2 which gives the results 






Fig. 2. 

for two different cathodes rather heavily coated with CaO. I mention 
the thickness of the CaO coating as I am of the opinion that it makes a 
difference. In my previous work on the mercury arc I used heavy 
coats of BaO on the cathode. 

It will be noticed that the lower parts of the graphs approximate 
more or less to straight lines. The straightness of this part of the graphs 
I have examined closely and find that in a great many cases it seems to 
be straight within the limits of observation. Had I taken care to glow 
well the cathodes used in Fig. 2 before I made those observations the 
lower part of the graphs, I have no doubt, would have been straight. 

In order to obviate the correction and uncertainty due to the drop 
in the cathode I arranged a revolving commutator so that the cathode 
was heated intermittently, and the potential between the anode and 
cathode was applied only when the cathode current was off. In the 
use of the commutator the greatest care was exercised to prevent the 
potential being applied even for an instant while the cathode" current 



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378 T. C. HEBB. [i^S? 

was flowing. The current was made and broken 60 times per second 
and the potential was applied a like number of times. This method is 
not favorable for studying the weak arcs produced with low temperature 
cathodes hence that end of the graph is not shown. Fig. 3 gives the 
results obtained with such a commutator when the cathodes were rather 
heavily coated with CaO. The two graphs are for separate cathodes. 

The graphs of Fig. 3 suggest that there is no significance, as far as 
these experiments go, in the potential difference of 4.9 volts. As a 
matter of fact it was only on rare occasions that I got an arc as low as 
4.9 volts with the present apparatus. And it should be stated that in 






Fig. 3. 

the experiments recorded in Figs. 2 and 3 the cathodes were heated 
until they melted. 

The graphs in Fig. 3 also suggest the idea that if the current could be 
still further increased the striking voltage would keep on decreasing in a 
linear manner with the current. I attempted to follow this line of 
reasoning by using tungsten coated with CaO but owing, apparently, 
to a chemical change between the tungsten and the CaO I was unsuccess- 
ful. With tungsten alone, however, I found that I could get the arc 
to strike at voltages much lower than I had obtained before. I am not 
prepared at present to say what is the lowest voltage at which an arc in 
mercury vapor using a tungsten cathode can be made to strike but I 
have got it as low as 3.2 volts. This was obtained with the commutator 
so that there is no uncertainty from cathode drop. Further I found 
that there was a linear relation between the current through the cathode 
and the striking voltage as was the case for platinum cathodes. It 
should be stated that the tungsten used was in the form of a strip as 
nearly as possible to the size of the platinum used. Fig. 4, graph a, 
shows tjie results for one cathode. Although only three observations 
were made before the cathode melted, it will be seen that they lie very 
close to a straight line. With the commutator I have found it impossible 
to make observations on arcs when I used low-temperature cathodes. 
Fig' 4i graph 6, however, gives the results with a tungsten cathode 
heated without the use of the commutator. In order to approximate 



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Na's^^'l ARCING VOLTAGES IN MERCURY VAPOR. 379 

the correction for cathode drop the cathode was constricted at the center 
so that only that portion of it was highly heated. It will be noticed 
that the upper portion of the graph is very steep, as was the case for 
platinum, and that then the graph becomes straight. The lowest 
striking potential observed was 3.9 volts but the cathode melted at 
about 30 amperes before other observations were made. If the straight 



> 






Amps, thru CuihoJt 

Fig. 4. 

portion of the graph is produced, however, it reaches about 3.2 volts at 
30 amperes. 

I have already suggested that the thickness of the oxide deposit on 
the cathode affected the value of the striking voltage. I had always 
followed the practice, unusual I think, of coating the cathode rather 
heavily. This was done by putting small pieces of the nitrate on the 
cathode and then heating them. In endeavoring to determine the 
effect of impurities in the oxide on the value of the striking voltage I was 
led to use much thinner deposits. I fpund immediately that there was a 
considerable change. In fact, it was found that the lowest striking 
voltage for thinly coated cathodes was in the neighborhood of 6.0 volts. 
This is shown in Fig. 5 which gives the data for two separate cathodes. 

8 

Fig. 5. 

In both cases the current was increased until the cathode melted. The 
two curves also show the variation caused by different treatment of the 
cathodes. In the case of the upper graph the cathode was used for the 



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38o T. C. HEBB. [HS^ 

first time, whereas in the case of the lower graph the cathode had previ- 
ously been heated to a high temperature and well freed of gas. In 
neither case was the commutator used but as only a small spot of CaO 
was used a fairly close correction for drop in the cathode could be made. 

Fig. 6 gives a comparison between the results obtained with two 
cathodes, one more heavily coated with oxide than the other. The two 
cathodes were initially of as nearly the same dimensions as they could 
be made. The commutator was used in both cases. The thinly coated 
one melted at about 25 amperes whereas the more heavily coated one 
melted at 27 amperes. In the latter case when the current was first 
brought to 27 the striking potential was 5.5 volts but as time elapsed 
the striking potential dropped lower and lower until it reached the 
minimum of 4.8 volts. Shortly afterwards the cathode melted. 

In some cases with coated cathodes the low striking voltage is only 
temporary. In one particular case, for instance, while studying the 
effect of vapor pressure on the striking of the arc, the arc suddenly 



:5 



Fig. 6. 

began to strike lower and lower until it reached 4.8 volts. The next day 
I obtained with the same apparatus a minimum of 5.8 volts just before 
the cathode melted. 

The graphs given in Figs. 2-6 show quite conclusively that for the 
higher temperatures and for the cathodes used the striking voltage is a 
linear function of the current through the cathode. As the cathode 
current itself is not the important factor, these results suggested that 
there might be a simple relation between the striking voltage and the 
temperature of the cathode. Rough experiments in which I used the 
melting points of various salts and metals convinced me that the tempera- 
ture of the cathode was, at least roughly, a linear function of the cathode 
current. It may be of interest to state in passing that the same appar- 
ently holds quite closely for a platinum wire in free air. This will be 
seen if the results of Langmuir given on page 413, Vol. 34, 1912, of the 



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Vol. XVI.l 
No. s. J 



ARCING VOLTAGES IN MERCURY VAPOR, 



381 



Physical Review, be plotted. The article referred to is on the con- 
duction and convection of heat in gases. 

To measure the temperature of the cathode more accurately I deter- 
mined the resistance of a portion of it at two known temperatures, and 
then made use of the fact pointed out by Langmuir that the temperature- 
resistance graph for platinum is straight above 1100° C. As I found 
that I could use the melting points of NaCl and K1SO4 most satis- 
factorily, I used these two temperatures, viz., 801° C. and 1070° C, 
and drew a straight line through them. This, of course, gives too low a 
value of the temperature for points above 1100° C. To correct for 
this, approximately, I drew another straight line between 1070° C. and a 
point which was 20° C. above the first line at 1900° C. This correction 
would vary somewhat with the platinum used but seemed from a study 
of the temperature-resistance curve for platinum to be somewhere near 
the truth. 

The resistance of the portion of the cathode used was determined by 
measuring the current through the cathode with a standard o.i ohm 
resistance and a potentiometer, and the drop across the portion used 
with a potentiometer. For the latter purpose two fine pin holes were 
made in the central part of the cathode about 0.5 cm. apart. Through 
these holes fine wedge-shaped strips of platinum foil were inserted until 
they were tight. The ends of these strips were cemented with platinum 
chloride to platinum wires and these wires led to the potentiometer set. 
The part of the cathode between the potential leads seemed to have a 
fairly uniform temperature. Small bits of fused sodium chloride and 
potassium sulphate were then used to find, in the usual way, the resistance 
of the cathode at their melting points. The results obtained for one 
cathode are given below: 



Substance. 


Amperef. 


Volti. 


Resittence. 


NaCl 


4.652 
4.636 
4.675 
4.656 


.2422 
.2400 
.2432 
.2433 


.05206 
.05177 


II 


.05204 


II 


.05226 








Mean .05203 



Substance. 


Amperes. 


Volts. 


Resistance. 


K1SO4 


5.710 
5.737 


.3513 
.3529 
.3511 
.3515 


.06152 


II 


.06151 


II 


i.700 
5.714 


.06160 


«i 


.06152 






Mean .06154 



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382 



r. C. HEBB. 



[i 



Sk 



With these two resistances and their respective temperatures the 
temperature-resistance graph was obtained as indicated above. 

Having obtained the above data a small thin spot of CaO was placed 
at the center of the cathode. This no doubt changed the temperature- 
resistance characteristics of the cathode, but the method was deemed 
better than the one in which the graph was obtained after the CaO was 
placed on the cathode. Of course, it was impossible to use the com- 
mutator in determining the striking voltage for any particular tempera- 
ture and hence an uncertainty is introduced in correcting for cathode 
drop. As the spot of CaO was placed at the center, the correction was 
always taken as equal to one half the drop over the cathode. The fol- 
lowing table contains the data obtained for the cathode whose resistance- 
temperature data was given above. The cathode was well heated before 
these observations were made. 



Amps. Thro. 
Cathode. 


P. D. 
VolU. 


Resist- 
ance 


Temp, of 
Cathode. 


Obs»d StrVg 
Voltage. 


Cathode and 
Lead Drop. 


Corrected 
StrlK'g Volt. 


6.197 


.4433 


.0716 


1630 K 


6.25 


1.81 


7.16 


6.519 


.4757 


.0729 


1670 " 


5.90 


1.95 


6.83 


7.046 


.5313 


.0754 


1740 " 


5.50 


2.15 


6.58 


7.703 


.6036 


.0783 


1818 " 


5.15 


2.40 


6.35 


8.210 


.6632 


.0807 


1890 


4.85 


2.59 


6.15 


8.576 


.7017 


.0818 


1925 


4.70 


2.72 


6.06 



The cathode melted shortly after the last observation was made. Both 
amperes and volts were observed with the aid of the potentiometer sets 
and are more accurate than necessary. The resistance has been calcu- 
lated with a slide rule. 

The relation between the temperature of the cathode and the striking 
voltage is shown in Fig. 7, lower curve. The upper curve is from data 

obtained with an entirely different 
^ athode. Both graphs show that 

there is a linear relation between 
the temperature of the cathode and 
the striking voltage of the arc. I have 
not data enough yet to say whether 
or not these two graphs should be 
coincident but there is a good pos- 
sibility that such should be the case as the errors arising from cathode- 
drop correction, temperature determination and effect of CaO thickness 
might easily, I think, explain the difference. If these two lines be ex- 
tended to cut the r = axis they do so at F = 11.2 and V = 14.0 
volts respectively. These two values are sufficiently close to the ioniza- 
tion potential of mercury vapor, viz., 10.5, to be, at least, suggestive. 






Fig. 7. 



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Nas^^^'] ARCING VOLTAGES IN MERCURY VAPOR. 383 

I have already pointed out that the lowest striking voltage for mercury 
vapor with a platinum cathode thinly coated with CaO is in the neighbor- 
hood of 6.0 volts. The data I have at present suggest a slightly higher 
value. And I have also pointed out that the striking voltage for mercury 
vapor with a tungsten cathode near its melting point is 3.2 volts. If 
these two voltages be plotted against their corresponding absolute 
temperatures, viz. 2028 and 3540, and the straight line drawn through 
them be produced to cut the T = o axis a value of 9.8 volts is obtained. 
This value is not very different from the ionization potential of mercury 
vapor. 

Now these data, admittedly imperfect, show that there is a linear 
relation between the striking voltage of the arc in mercury vapor and 
the temperature of the cathode for the higher temperatures. They 
further suggest that the decrease in the ionization potential is directly 
proportional to the absolute temperature, i.e., that the relation between 
the striking voltage and the absolute temperature of the cathode can be 
expressed by the equation V = 10.5 — kT, where ft is a constant. If 
the values for V and T at the melting point of tungsten be substituted in 
this equation a value of k is obtained viz., .0021 volts/degree. 

These results do not seem to admit of any simple explanation although 
at first sight they appear to do so. The fact that the decrease in the 
potential at which ionization takes place appears to vary directly with 
the absolute temperature of the cathode suggests that this decrease is 
due to the velocity qf emission of the electrons. Although it has been 
shown that the velocity of emission of the electrons is directly propor- 
tional to the absolute temperature, yet it has also been shown that the 
velocity is that of thermal agitation and hence would not be equivalent 
to more than a fraction of a volt at the temperatures used. 

As the mercury vapor in contact with the cathode must be very 
nearly at the temperature of the cathode, it is evident that the absolute 
temperature of the former would be directly proportional to the decrease 
in the striking voltage. But the same objection holds for this case as 
held for the previous one. The increase in the energy of thermal agita- 
tion of the molecules per degree is only about one sixteenth of the energy 
increase necessary to explain the phenomena. 

A few experiments were performed to ascertain if possible whether 
the cause of the low arc depended on the temperature of (i) the cathode, 
(2) the vapor, or (3) the anode. For this purpose the minimum striking 
voltage, i.e., the striking voltage just before the cathode melts, was 
determined for cathodes of widths varying from approximately 0.5 mm. 
to 7.0 mm. These experiments led me to believe that there was no 



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5KC09CD 



384 T, C. HEBB. 

relation between width of cathode and the striking voltage. The 
values obtained for all cathodes with thin spots of CaO on them were 
in the neighborhood of 6.0 volts. As the wider cathodes required very 
much larger currents to heat them, this would appear to show that it is 
the temperature of the cathode which is important and not that of the 
vapor or anode. As, however, no temperature determinations were 
made these experiments are not conclusive. 

Some further experiments were made with a hot anode. For this 
purpose two commutators connected to the same revolving shaft were 
used. By this means the anode and cathode could be heated simul- 
taneously and the voltage between the anode and cathode could be applied 
when no current was passing through either anode or cathode. Further 
by opening the appropriate switch the anode could be kept cool while 
the cathode was still heated. The only experiments I have performed 
with this arrangement of apparatus were those in which I used platinum 
electrodes. The cathode contained a small thin spot of CaO at its center 
and was separated 2-3 mni. from a clean platinum anode. Under these 
conditions I found that with the anode hot the striking voltage was in 
the vicinity of one volt lower than when the anode was cold. The fol- 
lowing data may make it clearer: 

Striking Voltage with Striking Voltage with 

Anode Cold. Anode Hot 

6.8 5.4 

6.5 5.2 

6.3 ....; 5.15 

6.25 5.05 

It may be necessary to point out that the different striking voltages 
with the anode cold were obtained by passing different currents through 
the cathode. 

From these data it will be seen that the heated anode causes a lowering 
of the striking voltage of about 1.3 volts. Further experiments on these 
very interesting phenomena developed the fact that although the striking 
voltage was lowered by the hot anode the amount of lowering was 
increased by shutting off the current through the anode. Parenthet- 
ically, I may add that I think that this effect is due to the change in 
density of the mercury vapor between the anode and cathode. This 
state of affairs, however, lasted only a short time and then the striking 
voltage gradually rose to its old value. Thus with the anode cold the 
arc struck at 6.7 volts in a certain experiment. The anode was then 
heated and the arc struck lower (I have not recorded the value in my 
notebook), but it struck still lower, viz., at 5.05 volts, immediately after 
the anode current was shut off. The striking voltage then rose slowly 



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Nas^^'l ARCING VOLTAGES IN MERCURY VAPOR. 385 

to 6.7 volts. It was found that the amount the striking voltage was 
lowered increased with the temperature of the anode. Also, within 
limits, a short period of heating did not cause as low an arc as a longer 
period. Continued heating beyond a certain maximum of time did not 
further affect the striking voltage. Continued low heating did not 
accomplish as great a drop as continued high heating. The lowest 
striking voltage I obtained during the above experiments was 4.95 volts. 
It will be noticed, therefore, that a platinum cathode with a thin patch 
of CaO on it can, with the aid of a hot anode, produce an arc about as 
low as I have obtained with a thickly coated cathode without a hot 
anode. Whether these two phenomena are produced by the same causes 
or not, I am unable to say. 

At this point I was forced to drop the experiments for a considerable 
time but it was thought that the results would be of interest even in this 
unfinished state. 

The results embodied in this paper do not appear to me to have any 
simple interpretation. As long as the striking of the arc was obtained 
at a value equal to or higher than 4.9 volts it seemed possible that Van 
der BijTs theory of multiple collision in terms of the Bohr atom^might 
be the correct explanation. But even this explanation has been shown 
by Compton^ to be doubtful. That the density of the electron stream 
is very important I have shown previously. This is also shown by 
Fig. 2. As the temperature of the cathode rises from red heat the 
striking voltage drops rapidly at first as would be expected if density of 
electron emission is important. But for the lower part of the graph 
entirely different phenomena seem to be operating. For this part of 
the graph it seems possible that space charge might be influencing the 
results but, if so, apparently in no simple manner. .When the arc 
strikes, the operating voltage is still lower, which is also in line with the 
idea that space charge is active in these phenomena. In this connection 
I may state that I have had an arc operate with tungsten cathodes as 
low as 1.7 volts. 

In order to explain the striking of the arc at potential differences con- 
siderably lower than 4.9 volts and possibly for the explanation of low- 
voltage arcs it would seem as if one would be forced to assume inelastic 
collision and gradual accumulation of energy in the atom. 

There are other factors, however, which, I believe, have to be con- 
sidered, such as contact potential difference and impurities. I have 
previously shown that if sodium or potassium are present with mercury 
the arc strikes and operates lower than with pure mercury and that the 

» Phys. Rev.. Feb., 1920. 



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386 ARCING VOLTAGES IN MERCURY VAPOR. 

lines of the sodium or potassium may not appear. I have also tried 
putting a little sodium hydroxide or potassium hydroxide with the CaO 
on the cathode. The sodium hydroxide causes the arc to strike at 5.0 
volts whereas the potassium hydroxide causes it to strike lower than 
5.0 volts. In the first case the D lines of sodium appear with the mercury- 
lines, in the latter case only the mercury lines appear. 

The results with the hot anode suggest that something in the nature 
of an impurity has been evaporated from the anode, and hence changed 
the contact potential. The fact that it takes some minutes for the 
striking voltage to regain its former value when the anode current is 
shut off would lead one to think that some deposit is accumulating on 
the anode. It may be, however, that the extra heat has changed the 
internal energy of the mercury atoms. I have tried, also, to picture a 
redistribution of current in the cathode due to the heat from the anode- 
As the hot lime has a negative temperature-resistance coefficient it might 
be possible for the calcium oxide to carry more of the current when 
heated by the anode and hence be at an even higher temperature than 
the platinum of the cathode. If such is possible this would also explain 
the lower arcs obtained with thickly coated cathodes. However, even 
if this were found to be true it would not be an explanation of the pro- 
duction and operation of these low arcs. 

University op British Columbia, Vancouver. B. C. 



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Na's^^'] ELECTRON TUBE, 387 



THE CALCULATION OF DETECTING AND AMPLIFYING 

PROPERTIES OF AN ELECTRON TUBE FROM ITS 

STATIC CHARACTERISTICS. 

By G. Breit. 

Synopsis. 

Calculation of the Detecting Efficiency of an Electron Tube. — The detecting efficiency 
of an electron tube is calculated. In the calculation it is assumed that experi- 
mental knowledge of the static characteristics of the tube is available. The constants 
of the circuits used with the tube are also taken as known. From these quantities 
the average change in the plate current for a given amplitude impressed grid voltage 
is derived. The impressed grid voltage is taken to be of the form A cos <at where A 
is constant. The case when A varies slowly is also discussed. 

Calculation of the Input Impedance of an Elect/on Tube. — The input impedance of 
an electron tube is calculated for the case of both positive and negative grid voltages, 
no assumption being made as to the mathematical form of the tube characteristics. 

Generalisalion of the Concept of Internal Resistance and Amplification Factor. — 
The concept of the complex internal resistance is introduced in treating the ampli- 
fication due to a single tube. This quantity is defined by 



'--. 



\jCifo I 

where fp is the internal resistance. Ci the grid plate capacity, j — V— i. and 
w/2T — frequency. Similarly the amplification factor is generalized. (See (4.3)). 

Condition for the Vanishing of Incoming Signal. — The condition for the vanishing 
of the incoming signal has been worked out. For the case of zero grid current 
this condition is just satisfied by tubes obejring Van der Bijl's relation. 

It is also seen that the condition is not satisfied by the values of plate circuit 
constants predicted from the simple theory neglecting internal capacities. 

THE first rigorous calculation of the detecting action of an electron 
tube is to my knowledge due to Carson.^ Carson treats the 
special case of an electron tube used with sufficiently high negative 
grid voltage to make the grid current zero. He does not take into account 
the possibility of having a different value for the resistance of the plate 
circuit at high and low frequencies, as is seen from his formula. He also 
confines himself to the consideration of an electron tube for which Van 
der Bijl's relation holds for the plate current in terms of the plate and 
grid voltages. 

The following treatment concerns itself with an electron tube having 
' See Carson, Proceedings of the Institute of Radio Engineers, Vol. 7, April, 1919. 



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388 G. BREIT, [^^ 

three electrodes: (i) A cathode consisting usually of a wire heated to 
incandescence by an electric current. (2) An anode which is usually 
made of a flat or cylindrical metallic plate and (3) a wire control or grid 
which is placed between the cathode and the anode. 

In what follows I shall refer to the cathode as the filament^ to the anode 
as the plate, and to the intermediary electrode as the grid of the tube. 
The filament of the tube has two terminals which are used to heat the 
filament. It is clear that when the filament is heated by the passage of 
an electric current through it the potential of its two terminals is different. 
For this reason when the filament is used as a cathode we cannot speak 
of the potential of the cathode as a whole. However, if the filament 
current is known and if the potential of one of its terminals is known the 
orid plate Potential of all the remaining points of the fila- 
fi lament ^ n ment is determined uniquely. We thus choose 

arbitrarily as our standard the potential of one 
of the terminals of the filament and we shall 
refer to it as the potential of the filament. The 
grid and plate may in all practical cases be re- 
garded as equipotential surfaces. The terms 
*^' * "grid potential" and "plate potential" are thus 

clear. The difference between the potential of the grid and that of the 
filament we shall call Eg; similarly the difference between the potential 
of the plate and that of the filament will be denoted by £p. 

Experiments with direct currents show that two quantities Eg, Ep 
determine completely the currents which flow from the grid and from the 
plate inside the tube. If these currents, reckoned positive in the direc- 
tions shown on Fig. i, be called^J^,, Ip respectively we can write, 

J, = /(£„ Ep), 

Ip = ip{Eg, Ep), 

where/ and <p are functions of the two arguments Eg and Ep, The form 
of these functions can be determined mathematically with fair precision 
for some tubes. The general action of the tube, however, can be predicted 
without having an accurate knowledge of the mathematical law connect- 
ing Ig, Ip with Eg, Ep. 

We shall assume in what follows that these functions / and ^ have 
within the range considered a first, second and third derivative, all of 
these being finite and single valued, and the function itself with its first 
two derivatives with respect to each argument being in addition con- 
tinuous. 

We shall also assume that even for unsteady currents the equations (i) 



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JJSJ;-,^'] ELECTRON TUBE. 389 

give values of Ig and Ip which represent the current carried by conduction 
by the ions inside the tube provided Eg, Ep denote the instantaneous 
values of the grid and plate potentials. (The filament potential is taken 
as zero.) 

Before proceeding with the mathematical development of the problem 
I must point out the limitations put on this development by the physical 
assumptions made. There is no doubt that all of the functions considered 
are finite and single valued. The differentiability of the functions can 
be doubted in some cases especially in that of the grid current. Thus 
it is known that there is an essential distinction between the behavior 
of the grid current for positive and negative grid potentials. The grid 
current for negative potentials grid is zero to all intents and purposes. 
Thus at Eg = o one would be unable to define the derivative: dIg/dEg. 

Fortunately this difficulty is only formal in character because a suffi- 
ciently close examination of the static characteristics shows that there 
is some grid current even for negative grid potentials. So that dIg/dEg 
always exists. Thus we will be safe to apply our theory provided we 
shall recognize by means of our instruments currents and potentials so 
small that dlg/dEg is continuous. 

Another possibility of a break down in the theory is offered by our 
second assumption. In fact it is conceivable that the space inside the 
electron tube may have a resonant frequency. This frequency may be 
fixed by the dimensions or shape of the space between the electrodes. 
If such is the case /^, Ip are no longer single-valued functions of Eg, Ep 
when unsteady currents are considered. In fact one would expect to 
have here a dependence of /^, Ip either on dEgjdt, dEp/dt or on the previous 
history of Eg, Ep, 

Such resonant effects have been described by R. Whiddington^. They 
come into play, however, at frequencies very 
much higher than those ordinarily employed 
in wireless telegraphy. Also these effects are 
practically absent in high vacuum tubes. 
Thus here again we have a wide range within 
which our theory applies. In many cases 
electron tubes are used as detectors in di- F»g- 2. 

rection finder circuits. If such is the case 

they are connected across the terminals of the tuning condenser the 
connections being as in Fig. 2. In this type of connection the electro- 
motive force is induced in the coil. The reader will see without difficulty 
that this circuit is a special case of a slightly more general one drawn in 

» Radio Review, i, 53. I9i9« 



T 

detector 

i 



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390 



G. BREIT, 



rSsCOMD 

ISbroes. 



Fig. 3. Here e represents the place where the electromotive force is 
induced; Zg' takes the place of the direction finder coil; Zg" replaces 
the tuning condenser. For generality Zg was introduced into the circuit 
so as to include the possibility of a blocking condenser and grid leak. 
The capacities Cu c^ represent the effective capacities between the elec- 
trodes. There is, of course, a third capacity between the filament and 
plate. But this can be incorporated as part of the circuit Zp, The 
diagram of Fig. 3 includes most of the circuits which are used with 
electron tubes. The only essential type of connection left out is that 
in which there is inductive coupling between the plate and grid circuits. 

Notation. 
We shall distinguish between the behavior of the various circuits 
Zgj Zi\ Z^"f ^p at different frequencies. Thus we shall not assume 
that a definite resistance can be assigned to any one of these, because 
experiments show that such an assumption is illegitimate. Since it is a 
difficult matter to give in general the relation between the properties 
of an electric circuit at various frequencies we shall content ourselves 
by taking the impedance [meaning thereby R+jX(j— V— i), R 

denoting the resistance, X the 
reactance] of a circuit as a func- 
tion of the frequency which is 
known either experimentally or 
by computation. These complex 
values of the impedance at 
frequency c«>/2ir we shall write 

j£l g^ , j£l gf^ , j[t gff^ , j£l p^ , etC. 1 tiQ 

real part of these expressions 
, /j\ (i,e.f the resistance) will be writ- 
ten Rg^t Rg'tti Rg'^ttt Rpu and 
the imaginary part (i.e., the re- 
actance) will similarly be de- 
noted by Xg^f Xgt^y Xgff^^ Xp^, 

We will not be concerned in 
this problem with transient phe- 
nomena. If therefore the impressed electromotive force is periodic or if 
it consists of a sum of several periodic electromotive forces all the cur- 
rents are periodic or are sums of periodic functions the periods of the 
electromotive forces and the currents being equal. 

It is convenient for the mathematical treatment to represent the cur- 
rents and potentials as Fourier series. 




Fig. 3. 



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Nas^^^'l ELECTRON TUBE. 39 1 

We shall first treat the case when the electromotive force impressed 
{e) is of the form A cos tat. Then all the currents and potentials must 
be Fourier series in (at. Thus any one of these quantities is of the form 

Jo + Ji cos (at + 62 cos 2(at + • • • + ai sin w/ + aj sin 2«/ + • • • 

= 60 + 2(6« cos m(at + a^ sin moit) 

= 60 + s^^^"*-', 
where 

and where the real part only of the expression on the right is to be taken. 
Using this complex notation we can write 

and similarly for all other currents of Fig. 3. 
We shall now express the quantities 

Eg, Ep in terms of /g, Ip and e. 
We have 



JCi^ 



Zg^{Ig^ +*!•"■ hu) 



where the currents are as on the figure the positive directions being those 
of the arrows. (The currents are written to satisfy the first of Kirchhoff 's 
laws.) Solving these equations we find 



JCi(a ^ 



+Ipu-7^ 



5,« + (Zp.+j^)(Z^.+Z^.«+5Jci«) 

Zp^K>2^ 



(I) 



\ JCi(a J\jct(a *"• Z^^+Z^.«+5,«jci«/ 



Zgf^ +Zgff^ +jCl(aSt^ 



- "TZp^Ip, 



jcto "• Zg,^+Zg..^+Su.jci(a 



where 52^ = Z^/^Z^//^ + Zg^Zg,^ + Z^^Z^/^.^The complex expression 
for Eg^ is obtained as tiljcita while that for £p« is lu»ljci(a + t%^/jct(a. 



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392 G. BREIT. 

Performing the calculation we find 

(i.i) - - - - - - 

where 






(1.2) - ^Zgn^^ - _ 5l^m 



p,- = 






where 



^« 



We called the impressed electromotive force A cos «/. To each value 
of A there corresponds a definite plate current. It is clear that if il = o 
the plate current is steady. Similarly the grid current is steady. Let 
these values of grid and plate current be /^„ I^ respectively. For a 
value of A distinct from zero 

/, = /^ + A/„ 

/p = /,; + A/p, 
where AJ^, A7p are Fourier Series in w/. We shall thus write 
AJp = 60 + 61 cos 6)/ + h% cos 2wt + • • • + fli sin «/ + at sin 2«/ + • • • 
AJ^ = j8o + jSi cos 6)/ + jSa cos 2a)/ + • • • + ai sin «/ + aj sin 2w/ + • • • . 
Let us now write 

G\f^ = G\Jtr 






'U* 



then denoting by A£^, A£p the changes in the grid and plate voltage from 
the value corresponding to -4 = o we have : 



(G " \ 
«<+tan-»^j 



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Voi.XVI.-l 



,te.^ '•J BLECTKON TUBE. 393 

+G^r/3i COS ( «/+tan-» -^ j +a, sin ( «<+tan-» -~j j J 

+G^\ bi cos ( «<+tan-» -^ j +Oi sin I «/+tan-i ^=7 J J 

+Gtu\ /St cos f2«/+tan-> ^^)+«i sin f 2«/+tan-»^^j J 

+G,t-rJt cos r2«/+tan-« ^^J +a, sin faw^+tan-* ^T?^) J 

(1-3) ■^"■' , p „. 

A£p=P,^o+P^6o+Pu4 cosf «<+tan->-^j 

+P^ hi cos f «/+tan-i ^ j +ai sin ( «/+tan-' ^ j J 

+P,« 1 6, cos ( «<+tan-» -^ j +01 sin ( «/+tan-» y^ j J 

+P,fc. F/St cos (2«/+tan-» ^^r)+«« sin (2«<+tan-' yK^j J 

+Ppj, bt cos ( 2«/+tan-« ^^)+«» sin (2w/+tan-»-^^ j I 

+ •••. 

But our assumption as to the nature of the relationship between I,, 7, 
with Ep, Eg shows that for sufficiently small values of A£p, A£, 

where the first derivatives are to be evaluated at Ip — Jp^; Ig = /^ 
while the second derivatives are to be evaluated for some suitably chosen 
values of Ep, Eg in the intervals 

(£^ Ep, + A£p)(£,,. Eg, + AEg). 

If A£p, AEg are sufficiently small the values of the second derivatives 

are sensibly constant and can be taken simply as the values at (Ep,, Eg^. 

We can, therefore, regard all the derivatives as constant coefficients. 



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394 ^- BRRIT, 

If the mathematical expressions for Ip, Ig are known the derivatives will 
be obtained by ordinary differentiation. If no mathematical expression 
is available the derivatives are still easily obtainable from the graphs 
of the functions. 

First Approximation. Internal Resistance. Amplification 
Constant. Input Impedance. 

As a first approximation we can disregard the squares of A£p, AEg. 
Then 

Let^ us analyze AJp, A/^, AJSp, AE^ into a Fourier series, s ay S A/p^, 
SA/jK*, SAEp«, SAEa« where A/p« is of the form i4^*' (j = V— i) and 
where it is understood that only the real parts of the equations are to 
be considered. Since the equations (2) are linear we can write 



A/a- = ^^^^v. + ^^^a-. 



Combining these with (i.i) we have 

7 /'^Llp . ^r T^-^7 /'^p 4.^r "i 
Hence 

-* Pw -" ^« ^ > 

1 ot» — ^« ' ' 7 9 



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Vol- XVI.1 
No s. J 



ELECTRON TUBE. 



395 



where 









+ 



dig - x^r jL^-h.'B x^^^r 
d£p d£a 

aEp aEg • 

d£p d£g 
Before proceeding with the second approximation of the problem we 
shall interpret the equations given^ Let us consider the special case when 
Zgu — Zg>^ = o. Then (see 1.2) 8%^ = o, 






Gu» = i» 



Ggu = O, Gpu = o, 



(2.2) 



Z,, + ^ — 



P^ = o, 



Jr x>c* "" 



jct(a 



jc%(a 



From (2.1) and (2.2) we derive: 



dig 6/a jCt<aZj^ 



d{Ip,Ig) 



■*«» "" ^« 



a£g a£p I + jc^wZp^ ^(-Ep, Eg) I + jVawZp 



I + 



Zpt, 



dl. 



(2.3) 



I +ic,«z,«d£p 



ipM — ^1 



d/p jCi(aZp^ , ^/p 
^-Ep I + jct(aZ^ ^^0 



1 + 



dip 



I +jct(aZp^9Ep 

Also from (i') and (2.2) _ 

jcia)(i^ + Zp^IjJ) 



(24) 
Hence 



/a«# + *!« 



ii-=- 



I +jct<aZ, 

PM 



dip 



+ 



dip 



JCifa 



I +jCt<aZi 



-- + 



\ ^ jct(aj ^ jCi<a 



1 + 



dU 



I + jViwZp^ ^-Ep 



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396 G. BREIT. 

di, di, Zp, a(fp, J,) z ^/jcico 



d£, d£p- _i_ a(£p.£,)- , _^ 
Z^ dip 

I H ="" nE^ 

I +7Viw2p«^^p 

, . ? /afp afp af, a/, \ i af, z,. a(fp, /,) 

^ jc^ jct<a dEp 

The ratio KKIg^, + fO may be called the intrinsic input impedance of 
the tube because (neglecting the current flowing through the capacity 
Ci) Igu, + tu is the total current of frequency «/2x which flows from 
the outside circuit into the tube. I call the quotient KliJwm + *!••) 
the intrinsic input impedance of the tube in distinction to the true input 
impedance which is ej{lg^ + tu — *i«). There is really no advantage 
in knowing the true input impedance of the tube because the tube is 
always put in parallel with some other circuit, and the capcaity Ci can, 
therefore, be considered as part of that other circuit. This procedure 
as well as the fact that we incorporate the capacity from filament to 
plate in^Zp simplifies our expressions. 

Let Zu» denote the intrinsic input impedance. Then 

, V 5, ^ JCi<^ j c^ ^Ep 

x+Z f^ + ^ + ^ + 

^ ^ ^"^{dEp^ dEg^ dEp^ 



I dig a(7p, Ig) Zp^ 

'^ 3C%^ dEg "^ a(£p, Eg) jew 

An inspection of this equation shows that both the numerator and 
denominator are linear in Zp,^. This fact admits of an interesting inter- 
pretation. For^it is clear that the relation between Rp^ and Xp^ 
(Zp« = jRp« + jXp^ which will necessitate the real or the imaginary 
part of ZuM to be constant is such as to make the pts. (i?p«, Xp^ referred 
to cartesian axes lie on a circle. Thus the lines of constant input re- 
sistance in the Rp^, Xp^ plane, or constant input reactance are circles. 
Moreover all of these circles must pass through one point, viz., the point 
corresponding to Zi^ = oo . Again since in the Zi^ plane the lines of 
input resistance are orthogonal to the lines of input reactances the same 
must be true_in the Zp., plane. This gives a general picture of the 
variation of Z*^ with Zp^,. I have treated this matter in more detail 



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Jg;-^^^^-] ELECTRON TUBE, 397 

for the special case of negative grid voltage.^ It is seen, therefore, that 
so far as the general properties of the relationship between the plate 
circuit and the input impedance are concerned there is no difference 
between the case of positive and negative grid voltage. 

A more thorough investigation of the expression (3) will show, however, 
an essential distinction between the two cases. This is given by the 
value of Z^ for w = o. In fact this value is 



(3-1) Zi. = 



1 ^Pipc 



dip 
*dEp 



dl, d{I,, I,) J • 



If the grid voltage is sufficiently negative Ig is constant and therefore 
Zi^ — CO, In other words, there is no appreciable current absorbed 
from the external circuit when the frequency of the alternating current 
becomes sufficiently low and when Eg < o. 

On the contrary if jE^ > o then no matter how low the frequency used 
may be a sufficient amount of current is absorbed from the external 
circuit by the tube to oblige us to replace the tube for purposes of com- 
putation by the fictitious resistance Z*, given in (3.1). 

In most tubes dlp/dEp, dlg/SEg, dIp/dEg are positive while dlg/dEp is 
negative. Thus the Jacobian d(/p, Ig)/d(Ep, Eg) is positive and Zi^ 
is positive. 

The subject of input impedance has been worked out in detail for the 
case of negative grid voltage by Dr. J. M. Miller.* My formula (3) 
agrees with Dr. Miller's result if Ig = const, and if in Dr. Miller's 
formula Ci and Ci are put equal to zero. In fact both of these become 

^ + rjzp^ + ^) 

""" (iC + OZp^ + fp ' 

dEp^fp' dEg -dEp' 



provided we set 



The reasons why the internal resistance and the amplification constant 
K are to be identified with the expressions given will be discussed later. 
In order to compute the input impedance in the general case it is 
convenient to call 

^ See Bureau of Standards Radio Laboratory Report 5~V. 
* See Bureau of Standards Scientific Paper No. 351. 



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398 G. BREIT. 

"** ~ Va£p d£, "^ dE, "^ dEjl dE, ' 
a(£p, £, 



a(fp. 7,) /d7p . 



37, /a7, 
~ a£,/ d£, • 



Then 



I 

dE, 



''{^'■+]t) 



+1 



Writing 









RL = ITI ; X. j = — o .\r' , where 



(3.2) a = i^.r,+^, ^.,^^.^d^, 

7 = fp + A^R^ + 5 c5' ^ = "^^^^ " G^ " -^S' 

It is thus seen that a knowledge of the four derivatives dlp/dEp, dlp/dEg, 
dIg/dEg, dEg/dEp of Ct and of 2?p^, Xp^ is sufficient to enable one to 
calculate the input resistance and input reactance. We can thus con- 
sider the problem of input impedance as solved for both positive and 
negative grid voltages. 

Computation of Current in Plate Circuit. 
In many cases it is necessary to know the quantity Ip^ — lu because 
this, to a first approximation is the current in Zp. Such is, for example 
the case of a transformer-coupled amplifier. Now from (2.3) and (2.4, 

•7 . — jC2<ae^ Ip^ 



I +jC2(aZp^ I +jCt(aZp^ 



(4) 



dip dip jCt(a 



I + jCi<»)Zp^ 



_jC,„+'Il.J^lA±JC^^ 



J _l Zpv a7p 

i+iC,«Zp.a£p 



7 ^JjL 



I + jCiuZj^ + Zp„ r^ 



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No's^^'] ELECTRON TUBE. 399 

This simple relation connects the current through Zp with the voltage 
from the filament to the grid of the tube. It is seen that dIg/dEp, 
dIg/dEg do not come into this expression as could be expected. If Ct<a 
is sufficiently small 

(4.1; ij»i# — *!•. = «« 



where 



^^^dEp 



^ dEgf dEp ^^ " dip ' 



dEp 

A simple interpretation can be given to this last expression. In fact 
it shows that if Cs is negligible the current through Zp can be imagined 
as due to an electromotive force Ki^ acting in series with Zp« and a 
pure resistance, fp inside the tube. The positive direction of this electro- 
motive force is visibly in the direction from filament to plate outside 
the tube. For this reason we can call K the amplification factor and r, 
the internal resistance of the tube. We note the fact that Van der 
Bijl's relation is not used in making these definitions. 
If C% is not negligible we can still write (4) as: 



and writing 

(4.2) 





g, 


^^^ ir 
dE,-^ *" 


»*. 


z^ 


1 I 




I 


■r M^^'' 



Thus i^ may be spoken of as the complex internal resistance of the 
tube and ^» as its complex amplification factor at frequency o)/2x. 



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400 G, BREIT. 

It is of interest to note the connection between f^, and r^. For 
obviously 

I 



^+Vj^ 



rp I jCt<a 

This shows that the complex internal resistance can be obtained by imagining 
the capacity €% connected in parallel with the internal resistance rp. 

Second Approximation. 
Having calculated our quantities to the first order we can proceed 
to the calculation of 60 and ft). From equations (1.3) we find that the 
constant terms of (AE^)*, (A£g(A£p)), (A£,)* are neglecting quantities 
of higher order than the second. In (A£g)^: 

+ Ap.iGJGJ + GJ'Gu.") + Aa,{GJ'GJ - GJGJ') 
+ Ab,{G^'GJ + GJ'GJ') + Aa^{G^"GJ - G^'GJ') 
+ (- «iOi + fiibiKGJG^' + GJ'GJ') 

(5) + (l8iai - cibiKGpJ'GJ - G^'GJ') = 2J?„. 

In 2A£,A£p: 

A*{P\JGiJ + P\J'G}J') + APi[GiJPga' + Gu/'Pgm 

+ PiJG,J + Pim"G,J'] + Aai[PtJ'GiJ — PeJGut" 
+ P\JGqJ' — GgJP\J'\ + Abi{GiJPpJ + GuJ'PpJ' 
+ PiJ'GpJ' + PiJGjJ) + AaiiPfJ'GiJ — PjJGiJ' 
+ G^"PJ - GJPJ') + (P.<.'G,„' + PJ'G,J')(fix* - a,») 

+ (ai&i — o.iPi)(GgJ'P,J — PpJ'GfJ + PgJ'GpJ — PfJGpJ') 
+ (fi,b, - a,a,){G,JP^' + G,„"Pp." + P,„'G;h.' 
(5-1) + P,<."Gp.") = 2J?„. 

In (A£,)« = ^^ + ^* (i3,» + «,«) + ^ (61* + a,«) 

+ ^/3,(P,.'PJ + PJ'PJ') + ^a,(P^"Pu,' - P..'Pu.") 
+ AbxiP^'PJ + PpJ'Pu") + Aa,{P^"PJ - Pp„'Pu.") 
+ (jS,6i - a,a,){PJP^' + PgJ'PJ') 
(5.2) + OS,a, - aM){PvJ'PJ - PvJPoJ') = 2Ppp. 



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Jgj-,^'] ELECTRON TUBE. 4OI 

These expressions are calculable if we content ourselves with using 
values of ai, bu ecu Pi as obtained by our first approximation. 

In most practical cases the expressions for Rgg, Rgp, R„ simplify 
considerably, but for the sake of generality I preferred giving their 
complete expression. 

Identifying now constant terms on both sides of the equations 

we find 

where 

^' " dE,* ^" ^ dE^E, ^" ^ dE,* ^"' 

^' ~ dE* ■"" ^ d£,a£, ^"' ^ BE* ^"' 
Solving these two simultaneous equations in b, fi, we obtain 

y ^''dE^' ^^ dEj y-^'» 3E, ~ ^" dE'J 

_(p ^JjL,r ^-LL\(p'^4.r ^-^\ 

\ '*dE, ^ ^"dEj V^dE, "•" ^"dEj 
^'V-^'*dE^-^'*dEj + ^'V''dt-^^'-dEj 

(j_P ^Jz_r ^Vt p ^-Ll r ^-^\ 

V ^"dE, ^"dEjy ^"dE,~^"dEj 

(p ^JtL4.r ^Vp ^4.r ^^ 

~V"dE,'^^'idEjV''dE,^^'*dEpJ 

The first of these expressions enables us to calculate the average change 
in plate current due to the electromotive force, A cos ut, impressed in 



A) 



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402 G. BRBIT. KSSf 

series with Zg\ In a similar manner the second equation gives the 
average change in the grid current. The amplitude A enters in these 
equations only through Cp, Cg which are homogeneous linear functions 
of Rgff, Rgp, Rpp. Since ai, jSi, au bu are as a first approximation pro- 
portional to A it is readily seen from (5), (5.1), (5.2) that Rgg, Rgp, Rpp 
are proportional to A*. Hence our expressions for &o» Po are proportional 
to A*. In general, of course, there is no reason why this law should be 
strictly true. But it is true that the smaller A the more nearly 6o» ft 
are proportional to A*. 

One of the fundamental assumptions in our discussion was that the 
electromotive force A cos ut has been impressed on the circuit so long 
that the effect of the initial conditions has been obliterated. The time 
necessary for this is generally very small. Let us change A slowly 
enough to justify us in considering all of the currents at any instant as 
having values identical with the values which they would have if A 
had had the value which it has at that instant during an infinite time 
before the instant under consideration. If such is the case the value of bo 
at any instant is proportional to the value which A has at that instant. 
Thus, if A should vary as i + K cos pt where p is sufficiently small to 
secure conditions discussed above, the average change in the plate current 
will vary as I + (K^/2) + 2K cos pt + (K^/2) cos 2pi. 

Special Cases. 

The expressions (5.4) apply to the most general case under con- 
sideration and enable us to calculate frot Po when the E.M.F. impressed in 
series with Zg' is known. We have shown, however, how the action of 
the tube on the currents in the circuits Z^, Zg", Zg' can be computed by 
endowing the tube with an input impedance. Since our expressions for 
Rpp, Rpg, Rgg iuvolve only the squares of first order terms in A we can 
for convenience of computation divide the problem into two parts. The 
first will concern itself with a calculation of the voltage from F to G 
account being taken only of first powers in A. The second will deal 
with the calculation of bo assuming voltage as known. Using formula 
(3) we have no difficulty in solving the first phase of the problem. 

In order to deduce a solution of the second phase from our general 
expressions we imagine a case when Z^« = Zg^ = o. Then equations 
(1.2) simplify as in (2.2) and J^„» Ipi^ are given as in (2.3). Also from 
(5)» (5.i)» (5-2) we have 



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NoTs'^^] ELECTRON TUBE. 4O3 

2Rpv ^^A* + ^ (ax* + 61*) + AhiPj^'PJ + P^"PiJ') 

+ Aai{P^"PJ - Pp^'Pi.") . 
But it follows from expressions (2.2) that 

PJ « + Ctf^PpJ' and Pi«" = - Cti^P^'. 
Hence 

PpJPhJ + PpJ'Plm" = o 

and 

i^p» -Pi^ ~" Ppm Plm = C^<aPpt?» 
Thus 

2i?pp = — ^* + ^ (^1* + 61') + ^aiC,«Pp.«. (5.5) 

We note that au Pi do not occur in these expressions. Now (2.3) can 
be written 

X hm ~" Cm m v ^ ^ Cm 



_ (K + Ct<»P^") - jCtcoPJ 

~ " r — P ' — iP " 



91 



(r, - P,jy + PpJ'* 

. P^"(K + Ct<^P„") - CMr, - P,J)P„' 

(fp - Ppjy + Pv»"' 



_. [K(r, - P^') + fpCtoP^"] + j{KPpJ' + Ct»Pp* - r,Cta>P|H.1 



(rp - PpJY + Pp "* 



pot 



In our case 
Therefore 



bi^A 



ai — A 



g« = i4 (cos iat + j sin w/)* 
Jf (rp - PvJ) + fpCti^PvJ' 






ifp - Pp«0* + p. 



//2 



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404 ELECTRON TUBE. 

Also 

AibiP^' + aiPJ') 

- KP^* + Kr,P^' + 2r,C,<oPJP^" - Cto>P^"P^* 
(r, - Pp.')* ■¥ P^'" 
A*[ r P ». r,*C,.^P^" - KP^* + Kr^J l 

= ^.[-c,«P. + ^r,-P^r + p^"* — J- 

We thus derive from (5.5) and (5.5)' that 

p _d! J? A*r, *C»wP^" - KP^* + KfpPJ 

"'4' ^"-2 (,, _ p^/). + p^..« • 

because PJ = Ci(oP„", 

K .^V«^P « + d!p .(g + C««Pp-'0* + C,*«»Pp,« 



4 - 4 - (^^_p^/)» + p^ 



//I 



f S.6) H Caw "p-* s 

,^p , K^ + VCV 
4 '"(r,-Pp.')* + Pp."** 
Now from (5.4) and (5.3) it follows that 

60 = appRpp + OpfRpg + OlfgRgg, 

where 

A«,p = ^,X + ^,/., where ^ = » " -P^^i; " G..^, 

^ "" " d£,a£, ^ ■•" a£pa£, ^' ^ ~ ^" d£p ■*" ^'•a£, ' 

A' _^^x^!!Ll 

^""~d£,«^''"d£,*^* 
and 

V '•a£p ^ ''••d£ J V "a£p ■•■ '''*d£p; • 

Using the values of 2?p„ Pp,, P,j obtained in (5.6) we have 



A* , A* rp*C»«P^" - KPpJ + KrpPpJ 

I/O = a,| - 

(5.7) 



On — Ola a r OCnn « 

" 4 ^ " 2 (fp - p,„')* + Pp-"* 



A> , Ji:« + r,»-C»V 

PP ^ •'^P« , T, /N. . », „t' 



+ «PP— PP-* 



4 -- (fp - P,„0* + Pp 



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J^J^^] ELECTRON TUBE. 4O5 

This expression shows the nature of the dependence of the rectified 
component of the plate current on the constants of the plate circuit. 
In fs^ct the quantity 

p s =s 



Z^ {JCK^T^ 

can be seen to be the negative of the impedance which would be ob^ined 
by connecting the capacity Ct across the plate circuit impedance Zp^. 
If Pj^ is very large the predominating terms in (5.7) are 

At Kit A* 

42 4 

It is seen, therefore, that in general there is no reason why fc© should 
become zero when Pp^ «= oo . It is also seen that on account of the term 
fp^Ci^u^ multipl3ring into app even if it were possible to make fc© = o by 
Ppm = «> for one value of w this in general would not be true for a different 
<a. The condition which is necessary and sufficient to make bo =^ o 
when Ppm = «> for the case when r^C^df is negligible in comparison to 
K^ is agg — 2Kagp + appK} = O. 

Case of Negative Grid Voltage. 

It is of interest to see how our equations reduce in the case of negative 
grid voltage when Ig * const. = o. In this case 

y/p dUp dUp 

Z^ dEp^ dEpdEg dEg^ 

iA — I "t" f CCpp — y 9 apg « „ f agg — ^ . 

''' 1+^ 1+^ 1+^ 



r 



Hence 



p 



^^dE^E, {r,-Pjy+P^"* 



It is convenient to write Z„ = — P,„ — R^ +jX„; R„, X„ being both 
real. Then 

V ^ "•" fp / "• AUE," ^ dE,dE, (fp + 2?.Z* + XJ 

m,ZJ{K* + ri*Ct*<^) l 



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406 G. BREIT. 

of course (5.7 
(5.7)' fco = — [aa#-2a, 



Similarly of course (5.7) could be written 

fp*Ct«X. + KZJ + KfpIL 



(fp + ILy + XJ 



It is of interest to investigate the conditions for which fro can be made 
equal to zero or else to reverse sign by a proper choice of R^ and X^,. 
Clearing fractions 

{RJ + XJ)(a,„ - 2Ka,p + a,,{IP + fp'C'o,*)) 



fco = 



^ A} + 2fpR^{agg — Kagp) — 2agj^p*Cto)X^ + r^OL^t 

'" 4 (fp + i?-)* + X.» 

If agg — 2Kagp + app(E? + r^C^df) + o the denominator cannot be- 
come infinite without making the nimierator infinite and of the same 
order. Hence excluding the case mentioned the condition is that the 
equation 

{RJ + XJ){agg - 2Kagp + app{K} + tp^C^^of)) 

+ 2rp{agg — Kagp)R^ - 2a^pfp*CswX« + fp^agg = o (6.0) 

be satisfied by a possible pair of values of R^ and X^,. The equation 
written is the equation of a circle in Cartesian codrdinates. This circle 
is real if 

- rp^aggiagg - 2Kagp + app{Kt + fp^CiW)) + fp^iagg - KagpY 

+ clqv^vC^^^ > o or ttgp* > ag^pp. (6.1) 

This therefore is the condition which is necessary in order that it be 
possible to reverse the sign of 6© by merely changing the plate circuit. 
If the grid voltage is negative this condition becomes 

bHp bHp 



\dEpdEg) 



^ dEg'dEp^' 



It is remarkable that for tubes obeying Van der Bijl's relation 

\dEpdEg) ^dEg^'dEp^' 

This corresponds to the case when circle (6.0) collapses to a point. Thus 
bo can always be reduced to zero but cannot be made to reverse sign. 
As a matter of fact the circle (6.0) reduces in this case to 

Thus fco = o when 2?« = o, 

X -^- 

C2W 



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nS"s?^^''] electron tube. 407 

This explains why for very high values of i?^, fco has been observed to be 
diminished but not quite to zero. 

Proceeding now with the special case of tubes obeying Van der Bijl's 
relation we have 









In particular if Ct is very small 

and 

^ A^ dE* 

60 = — 



^{^i+^Yr, + R^Y + X^*] 



Johns Hopkins Univbrsity, 
March, 1020. 



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408 E. 0, HULBURT AND G. BREIT. [|S» 



THE DETECTING; EFFICIENCY OF THE SINGLE 
ELECTRON TUBE. 

By E. O. Hulburt and G. Brbit. 

Synopsis. 
Definition of Detecting Efficiency, — ^As a definition of the detecting efficiency 

A* 

lim r— is taken. Here fro is the average change in the rectified component of the 
oq 

output plate current cmd A is the amplitude of the input grid potential. 

Derivation of Theoretical Formula. — ^A theoretical formula is derived for the 
detecting efficiency. (See formula 12). 

Measurement of Detecting Efficiency. — Measurements of detecting efficiency 
were carried out by means of a condenser potential-divider and a sensitive quadrant 
electrometer. 

Verification of Theory by Experiment. — By the measurements performed the theory 
has been verified qualitatively. An attempt to verify the theory quantitatively 
showed the necessity of taking into account the capacities between the tube elements. 

Application to Armstrong's Tuned Plate Circuit. — The sudden drop in signal 
strength observed with Armstrong's circuit has been explained by the above theory. 

I. Introductory. 

IN a previous paper by the authors,^ it has been pointed out that the 
detecting efficiency means, in general words, the efficiency of an 
amplifier to render a weak signal intelligible. It was shown that the 
detecting efficiency depended upon the relation between the input grid 
potential and the resulting output plate current. In the case of the 
high frequency transformer-coupled amplifier the detecting efficiency 

was defined by the relation lim -jj where A and bo are the amplitudes, 

respectively, of the input grid potential, and of the rectified component 
of the output plate current. Experimental methods of measuring fco 
and A were devised, and the detecting efficiency was thus determined 
by direct measurement. In order to arrive at a complete understanding 
of the detecting efficiency, it is necessary to know how the detecting 
efficiency depends upon the characteristics of the tubes and upon the 
constants of the circuits of the amplifier. The present paper takes up 
this phase of the problem for a simple case and describes an investigation, 
both theoretical and experimental, of the detecting efficiency of a single 
electron tube. A theoretical analysis, in which certain simplifying 
» ''The Detecting Efficiency of the Electron Tube Amplifier." (As yet unpublished.) 



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noITs?^^'] Single electron tube. 409 

assumptions were made, was carried out which yielded an expression for 
the detecting efficiency of the tube in terms of the constants of the tube 
and the circuits. Experiments were then performed to test the theory. 

2. Theoretical. 

In the current literature on electron tubes Van der Bijl's* relation is 
usually taken as the starting point in the derivation of the concept of 
the internal resistance of the tube. This procedure is unnecessarily 
special, for the behavior of a tube may be represented by an amplification 
factor and an internal resistance even though it does not conform to 
Van der Bijl's relation. 

The following treatment considers only the case of negative grid 
voltage i.«., Eg < o. In this case the grid current is zero. A more 
general treatment of the problem will be taken up in a future paper. 
It is assumed that the plate current Ip is a function only of the plate 
voltage Ep and grid voltage Eg. We write 

Ip^fiEp^Eg). (I) 

It is assumed that this function within the range considered has first, 
second and third derivatives, and that the function and its derivatives 
are finite, single-valued and continuous. It is necessary to specify 
accurately the conditions just stipulated because there are cases for which 
these conditions do not hold. For example, the recent experiments of 
R. Whittington* show clearly that there are resonance effects of the 
positive ions within the tube. For frequencies close to these resonant 
frequencies it is not legitimate to say that Ip is a single-valued function 
of Ep and Eg only, because it depends on the time rate of change of these 
quantities. But these frequencies are so high that at the ordinary 
frequencies used in radio one is not troubled by the complex effects 
observed by Whittington. 

Denoting by Ax the change in any quantity ac, the expansion of (i) is 
written 

Mp = Ip{Ep, + A£p, Eg. + AEg) - Ip(Ep., Eg.) 

^^^ AT? J-^^'aP JL^^^^^ (AT?\^ J^ ^'^^ AT? AT? 

I S^T 

+ 2 64'^^'^''' •- ^'^ 

Epo and Ego are the values of the plate and grid voltages, respectively, 

> Proc. Inst. Radio Eng.. 7. 97, 1919. 
'Radio Review, i, 53. 1919. 



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41 E. O.'HULBURT AND G. BREIT. [^ 



;COND 



when there is no high frequency voltage impressed on the grid* The 
values of the derivatives in (2) are to be evaluated for Ep = £p, and 

Eg = £y,. 

It is assumed that we deal with small values of AEg and A£p, so that 
the differentials in (2) of higher order than the second can be neglected. 
It is also assumed that the internal capacities of the tube are negligible. 

Let us assume that the grid voltage varies with the time according to 
a sine law. So that 

AEg = A cos w/. (3) 

Then after initial conditions have been obliterated, the plate current 
can be expanded as a Fourier series in w/. 

Alp = bo + bi cos w/ + 62 cos 2wt + • • • 

+ ai sin w/ + ^2 sin 2a>/ + • • • . (4) 

It is seen that the constant term 60 means physically the rectified com- 
ponent of the change in the plate current. 

We denote the absolute value of the plate circuit impedance for the 
frequency fn{w/2v) by Z«, the resistance of that impedance by Rmt 
and the reactance by Xm- Then from (4) 



-AEp^ZA+Zibi cos ( w/+tan~i ^ J+Z262 cos f 2w/+tan"i -^ j 

+Ziai sin ( w/ + tan"^ ^ j+Z^^ sin ( 2w/+tan"^ -^ J . 
Setting (3) and (5) in (2) gives 
A/p=-^- j Zo&o+ZiJiCOsrw/+tan-i-^M+--- 

+Ziai sin f w^+tan"^ -^ j H | +^ A cos «/ 



(5) 



^2 dEp2 



ZJbo+Zibx cos f w/+tan-^ -^ j - 



+Ziaisin ( wZ+tan-^^ )+•••[ +1 T^.A^oos^o^i 



2dEg 



sin ( w/+tan ^ -^ J 
"dETdE^ cos (at j ZoJo+ZiJiCOs ( w/+tan""i '^P 

+Ziaisin L^+tan-i-^M+. • • [ 
+ etc. (6) 

The values of oo, ai, 02 • • •, Jo, &i, &2 * • •, are obtained by identifying 



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VOL.XVI.1 
No. 5. J 



SINGLE ELECTRON TUBE. 



411 



the terms of (4) and (6). In so doing we make use of the method of 
successive approximations and neglect higher orders than the second. 
Equating the constant terms we find 

A a»fp 

2 dEpdEg' 



60 = 






(biRi + aiXi) 



i+Zi 



dh 



(7) 



'd£p 



To find ai and 61 we identify the coefficients of cos w/ and sin w/ in (4) 
and (6) neglecting quantities of higher order than the first. This can 
be done conveniently by observing that the equations involved are all 
linear, the terms of (4) being 61 cos (at + a\ sin w/, and the terms of (6) 
being 

-^^-^[zi6iCos(«l + tan-i|j)+Ziais^ 



+ A cos (at 



We now introduce the symbol e = At^\ where i = V— i, and c isi 
the base of natural logarithms. Let (61 cos (at + ai sin (at) be the reaE 
part of Ipt^*, It is seen that Ip means the fundamental radio frequency 
component of the plate current. 
Then 



where 



Therefore 



where 



^' " BE ^'^^ "^d£/' 

V 



V=- 



ke 



fo = 



and 



-Zi + fp 
I 

dEg 



k = 17- 



dEj 

dl,- 

dE, 



(8) 



The expression (8) shows the relation between the internal resistance of 
the tube fp and dIp/dEp. It also gives a general meaning to the amplifica- 
tion factor k. It is to be noted that no use of Van der Bijl's relation has 
been made in the above derivation. 



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412 E. O. HULBURT AND G, BREIT, 

Further, expanding (8) we have 

, __ Ak[(rp + Ri) — iXi][cos <at + i sin wi] 



The real part of this is 
Ak 



[(fp + Ri) cos (at + Xi sin «/]. (lo) 



{fp + RiY + Xi^ 
Comparing (4) and (10) we see that 

. Ak{rj, + Ri) ^ . AkXi 



(rp + R,y + Xi« """ "^ (rp + i2i)« + X,^ ' 

Substituting these values in (7) gives finally the expression for bo/A\ 
which is the detecting efficiency for an amplitude A at frequency w/2x. 
It results that 



(-f)' 



I [(r, + 2?,)* + X,«] 
If the tube obeys Van der Bijl's relation 

d£p» dE^E, dE,*' 
In this case (ii) becomes 



fto ' dE, 



s: 



^* 4(i+|')[('-p + i?i)» + Xi«] 



(12) 



At the risk of repetition let us state again the meaning of the symbols 
used in (12). Zo, -Ri, Xi are the direct current resistance, the high 
frequency resistance, and the reactance of the plate circuit, respectively. 
fp is the internal resistance of the tube, fp and the derivative d^Ip/dEg* 
are obtained from the static characteristics of the tube. 

Formula (12) depicts the manner in which the detecting efficiency 
depends on the constants of the circuits and of the tube. In particular 
it states that 60 is proportional to A^ for a specified frequency. This 
has been shown to be approximately true by direct experiment. (See 
the curves of the paper by the authors referred to in Section I.) It 
remained for further experiment to determine to what extent the as- 
sumptions underlying the derivation of formula (12) were permissible. 
This is taken up in the following sections. 



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Vol. XVLl 
No. 5. J 



SINGLE ELECTRON TUBE. 



3. Apparatus. 



413 



The apparatus was arranged as shown schematically in Fig. i. The 
condenser potential divider consisting of the three condensers Cu Ct, Cz 
the inductance coil L' and the thermogalvanometer r,'were the same 
as that described in a previous paper by the authors (loc. cit.). By 
coupling U to a suitable generating set high frequency voltage of small 
known amplitude and frequency was impressed on the grid of the electron 
tube. The device for measuring the change in the rectified component 




rMAAAA 

LhhhHK 
R 



of the plate current consisted of a quadrant electrometer Q connected 
across a resistance i?, the potential drop across R due to the plate battery 
Pa being compensated by a potential divider Pi. This has also been 
described in the earlier paper (loc. cit.). The resistance R was a non- 
inductive resistance made of a dilute solution of copper sulphate in 
water. This was shunted by a variable condenser C. C" was a large 
fixed paper condenser having a low frequency capacity of about 2mP. 

In the plate circuit was inserted an inductance coil L shunted by a 
variable condenser C. The inductance of L was 1738/1*, its distributed 
capacity about i(>tniF, and its high frequency resistance at 1150 meters 
was 6 ohms. The condenser C was a General Radio Company Air 
Variable Condenser, Type 182 A. This had a shield which was always 
connected to the electrometer as shown in Fig. I. The electron tube was 
a Western Electric Company tube, Type V T I. The tube was used 
always with a filament current of i.io amp. and a plate voltage of 22.0 
volts. The negative terminal of a standard cell B, Fig. i, was always 
connected to the grid. A high resistance leak Ri (about 2 megohms) 
kept the grid potential at a definite value. 



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414 



E. O. HULBURT AND G. BREIT. 



4. Experimental Tests. 
It IS seen that when Ri and Xi in (12) become sufficiently large bo/A* 
becomes very small. This was verified in the following manner : Keeping 
the current through T constant, i.«., A constant, the condenser C 
was varied and the electrometer deflections were observed. Curves i 
and 2, Fig. 2, show the electrometer deflection in millimeters plotted 



IHO 



100 



60 



20 



mm 




mo 



160 C 
Fig. 2. 



180 



200 >u/A F 



against the capacity of C in fifxF. Curve I was taken for smaller deflec- 
tions than Curve 2. Also in curve I the resistance R was about 21,000 
ohms, while in Curve 2 R consisted of 421,000 ohms in series with a pair 
of telephones. The condenser C was disconnected in the case of Curve 2. 
It is seen that in both cases the deflection dropped down for a proper 
value of capacity. 

The explanation of these curves lies in the fact that Ri and Xi become 
very large for certain values of C. This can be seen from the expressions 
for the effective resistance and effective reactance of the parallel combina- 
tion of an inductance coil having an inductance L and resistance R with 
a condenser of capacity C. If Re and Xe are the effective resistance and 
reactance, respectively, it may be shown that 



R. 



22*C»w» + (LCco« - ly 



X, = " 



2PCa> + Lw(LCc^-i)2 



(13) 



The maximum value o 1?, (when C is varied) occurs very nearly at 



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Vol. XVLl 
No. s. J 



SINGLE ELECTRON TUBE. 



415 



C = i/La)«. The value of R^ for this value of C is i/ROu)^ = U<a^lR. 
Using the values obtained by measurement in the case of the present 
experiment, namely, 2? = 6 ohms, L = 1.738 X io'm*» w == 1.63 X lo*, 



l65flO"'aTnp 
12 



8 ■ 



18 



20 



22 Ep 2H 
Fig. 3. 



26 volts 



the effective resistance is found to be 1.34 X lo* ohms. This is Ri in the 
notation of formula (12). 

In order to determine fp the static characteristic curves of the electron 
tube were drawn. This was done by measuring the plate current Ip 



Ep2H.5 
volts 




for various values of the plate voltage and grid voltage. The curves are 
shown in Fig. 3 and 4. 



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41 6 £.0. HULBURT AND G, BREIT. [^^? 

From the slope of the curve of Fig. 3 at the operating point dlp/dE^ 
was obtained. In obtaining the operating voltage Ej^ account was 
taken of the potential drop in the plate circuit resistance. The reciprocal 
of dlp/dEp gives fp, which was found to be 6.5 X 10* ohms. The high 
value was due to the use of a small filament current (see section 3). 

Returning to the experiment under discussion, R was 2.1 X 10* ohms 
and when C was set so that the combination of L and C were at resonance 
for the impressed frequency, we have 

Ri = 1-34 X 10* + 2 X 10* = 1.36 X 10* ohms 
and 

{Ri + TpY = 2.01 X io«. 

If now C were to differ from its value at resonance by 20ymF the values 
of R9 and X9 (as computed . from (13)) are 714 ohms and 3.12 X 10* 
ohms, respectively. Then 

Ri = 2.1 X 10* + 0.7 X 10* = 2.2 X 10* ohms 

i2i + fp = 8.7 X 10* ohms; Xi = Xe = 3.12 X 10* ohms; 
and 

{Ri + fpY + Xi^ = 8.55 X 10'. 

Hence the electrometer deflection must have decreased in the ratio 
of at least 

2.01 X 10^ _ 
8.55 X io» " ^'^5* 

This calculation applies to Curve I, Fig. 2. An inspection of the curve 
shows at once that quantitatively the simple theory presented above is 
not borne out by experiment, for the electrometer deflection at the 
minimum point is about one-eighth of the deflection at 20^nF from the 
minimum. The discrepancy is to be attributed to the neglect of the 
effect of the internal capacities of the tube. If these capacities are taken 
into account there results a formula which gives better agreement with 
the observations. This will be taken up in a future paper. It was 
possible to demonstrate experimentally that the larger the capacity 
between the grid and plate of the tube became the less marked was the 
effect of making Ri very large. This was done as follows: A variable 
air condenser (General Radio Company, Type loi L) was connected 
from the grid to the plate of the tube. For a low condenser setting the 
electrometer deflection decreased perceptibly when Ri became sufficiently 
high. When the condenser reached a value of about ^oo^fiF the effect 
could no longer be observed. 

Another cause of error to be considered arises from the assiunption 
of Van der Bijl's relation. In the above case, however, the tube obeyed 



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Vol. XVI.l 
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SINGLE ELECTRON TUBE. 



417 



Van der Bijl's law closely, as seen from the curves of Fig. 4, and so the 
discrepancies cannot be attributed to a deviation from Van der Bijl's 
relation. 

There are various other factors which cause discrepancies between 
formula (12) and the measurements. An effect which is difficult to 



20 



10 



■TnTTl 




C 1 70 /A/A F 



100 MM- f 
Fig. 5. 



200 



take rigorously into account is that introduced by small capacities be- 
tween the various parts of the circuits. As an illustration of this effect 
the curves shown in Fig. 5 were drawn. In order to obtain the data for 

this family of curves the connections 
shown schematically in Fig. 6 were used 
in the plate circuit. It is seen that these 
connections differed from those used 
previously in that the electrometer was 
connected across all of the resistance in 
the plate circuit instead of across only 
a portion. 

By giving C smaller and smaller 
values the effect of a variation of C 
becomes less and less, as is seen from 
the curves of Fig. 5. These curves are 
plotted with electrometer deflections in 
mm. (which are proportional to the 
detecting efficiency) as ordinates against capacities of C in nfiF as 
abscissas for several values of C. The grid voltage was — 1.018 and 
the impressed wave-length 1,150 meters. It is noticed that the position 
of the minimum shifts. The explanation of the family of curves lies 
in the fact that the quadrant electrometer acted as a condenser. The 
position of the minimum of a curve occurs when J?i is a maximum. 




Fig. 6. 



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41 8 E. O. HULBURT AND G, BREIT, 

i?i is a maximum approximately when the sum of the resistances of the 
parallel combination of L and C, and the parallel combination of R and C, 
becomes zero. The total resistance of these parts in series depends on 
the setting of C because the eflfective resistance of the parallel combina- 
tion of R and C is 

R 

I +2e«C'V' 

If C is large the above quantity is small and consequently the total 
resistance of the plate circuit at its maximum is lessened because that 
resistance varies inversely with the resistance of all the parts in series. 

It was of interest to study the effect with a positive voltage on the 
grid. With £^ = + 1.51 volts curves similar to those of Fig. 5 were 
obtained and are shown in Fig. 7. It is seen that the electrometer 

IHOmtn 

130. A\ /^C''^°>^>^'' 

120 

2500 




lOO/iMF C 200 

Fig. 7. 

deflection, and hence the detecting efficiency, increased in absolute 
value, when Ri was increased, instead of decreasing as it did inthe case 
of negative grid voltage. It was observed, however, that the deflection 
in the case of a positive grid voltage and grid leak was opposite to that 
in the case of negative grid voltage. Thus, roughly speaking, the 
phenomenon may be explained by saying that there are two actions 
going on in the tube. One of these is due to the curvature of the grid 
voltage grid current curve, the other (the smaller of the two) is the same 
effect which has been studied with negative grid voltages. The effects 
on the average plate current due to these two actions are opposite. By 
making Ri very large we decrease the second effect and thus increase the 
absolute value of the deflection. Strictly speaking this way of describing 
the phenomenon is not entirely correct. It gives, however, an easily 
memorized picture of the experimental facts. 

We wish to point out the practical significance of the effects observed. 
We refer here to an effect frequently observed in the Armstrong regenera- 
tive circuit which to our knowledge has not been explained. In Arm- 



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}5JJ-^'] single electron tube. 419 

strong's circuit the parallel combination of L and C is used just as we 

used it in our experiments. It is found that as C is increased, starting 

with small values, the intensity of the sound increases up to a certain 

point where it suddenly drops. Using the same circuit which we studied 

above and connecting the tube to an antenna it was found that this point 

is precisely the point where, with the same plate circuit connections, the 

detecting efficiency was found to be least. Further, by taking out a 

sufficient amount of loading inductance in the antenna and then retuning 

with a larger series capacity the behavior of the circuit was changed 

altogether. The signal no longer increased with an increase of C but 

remained fairly constant except in a narrow region where it became very 

faint. This narrow region coincided with the position of sudden decrease 

observed before. 

Johns Hopkins Univsrstty, 
March, 1920. 



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420 K. MELVINA DOWNEY. ©SS 



VARIATION WITH PRESSURE OF THE RESIDUAL IONIZA- 
TION DUE TO THE PENETRATING RADIATION. 

By K. Mblvina Downs y. 

Synopsis. 

ResidwU Ionization in Closed Vessels: Experimental Method, — In order to throw 
light upon the type of radiation responsible for the residual ionization in closed 
vessels, the author has measured the ionization in a sphere one foot in diameter for 
pressures ranging up to 21,5 atmospheres. Any corpuscular radiation not absorbed 
in the ionization sphere has a penetration at one atmosphere equal to or greater 
than the product of the dimension oj the sphere and the number of atmospheres pressure. 
A special deviu was used to compensate for any fluctuations of the battery furnishing the 
high potential required for saturation. This consisted of two ionization spheres 
of the same electrical capacity which were connected to the opposite ends of a ten 
megohm resistance, the mid-point of which was earthed. Connections from the 
battery were made to the ends of the ten megohms. The final experiments were 
performed over water to eliminate any effect due to radio-active substances in the 
soil. 

Nature of Ionization Curve. — The shape of the ionization-pressure curves gives 
information as to the process of ionization. A discussion of such curves obtained by 
other observers has been given in connection with those of the author. The curves 
obtained in the present experiment give a linear relation. This indicates that the 
ionization is not due to a soft radiation from the walls of the sphere, but that it is 
due either to the direct action of a penetrating radiation without any effect produced 
by secondary j9 rays from the gas, or to a secondary » corpuscular radiation from the 
walls of the vessel. If the latter is responsible for the main portion of the ionization, 
the experiments indicate that it has a penetration of at least six and one half meters in 
air at atmospheric pressure. 

Diurnal Variation. — ^A few curves obtained during the preliminary observations 
have been given. 'Provided that the sky is not cloudy, these indicate the existence 
of a diurnal variation. 

Ionization in Air Due to Gamma Rays of Radium. — The ionization in a sphere 
one foot in diameter has been measured for pressures ranging up to 40 atmospheres. 
From four to twenty atmospheres a linear relation existed. The change in slope at 
twenty atmospheres to a value about six tenths of that at lower pressures may be at- 
tributed to some of the fi rays having completed their paths. At the high pressures 
there is a suggestion of an effect due to the secondary radiation from the air. 

Introduction. 
TF air or any other gas is enclosed in a metallic vessel, experiments 
-*- show that ions are produced in the gas at a constant rate even in 
the absence of any obviously apparent ionizing agent. The number of 
pairs of ions produced per c.c. per second varies slightly with the material 
of the vessel but over land is of the general order of magnitude of 10. 



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Na"^^*] VARIATION OP RESIDUAL IONIZATION, 42 I 

A part of this ionization is certainly due to the radiation from radio- 
active materials in the soil and the radio-active emanation in the air. 
That this source accounts for only a portion of the ionization is verified 
by the observations over the great oceans. Although the amount of 
radio-active material in these oceans and in the air over them is insigni- 
ficant, yet values of the order of 4 pairs of ions per c.c. per second are 
obtained in closed vessels over these oceans. Thus, Simpson and Wright 
obtained values ranging from 4 to 6 ions per c.c. per second over the 
Atlantic and Indian oceans;^ and, on the fourth cruise of the yacht 
Carnegie an average value of 3.8 ions was obtained over the Pacific and 
sub-antarctic oceans. Again, when the ionization vessel is shielded on 
all sides by water sufficient in thickness to absorb the known radiation, 
there is still a residual ionization as was first shown by the experiments 
of Rutherford and Cooke.* 

There are two views prevalent as to the origin of this residual ionization 
in gases. One attributes it to impurities in the walls of the vessel, 
and the other to a penetrating radiation having its origin outside the 
vessel. Much work has been done on this subject, particularly by Mc- 
Lennan and his students. An experiment of special interest is the one in 
which McLennan used an ionization chamber of ice. When this was 
placed over Lake Ontario, the ionization value obtained was only 2.6 
ions per c.c. per second. McLennan seems to favor the view that even 
this residual ionization was due to radio-active impurities in the ice, 
but no test for the radioactivity of this ice-receiver appears to have 
been made. 

Perhaps the most convincing evidence in favor of a true penetrating 
radiation in the atmosphere and against any explanation founded on 
the assumption of radio-active contamination is given by the balloon 
observations of Kleinschmidt and of Kohlhorster. The latter found, for 
example, that at an altitude of 9,300 meters, the value obtained for the 
residual ionization was 80.4 ions per c.c. per second.* The value at the 
surface of the earth would be only about 4 ions per c.c. per second if we 
neglect the contribution due to the gamma rays from the radio-active 
material in the soil, which contribution would be quite negligible at an 
altitude of even 2,000 meters. Kohlhorster 's results thus suggest a 
non-terrestrial radiation, increasing in intensity with altitude. 

» Roy. Soc. Proc., A. Vol. 85. pp. 196-198, 191 1. 

* Results of Atmospheric Electric Observations made aboard the Galilee (1907-1908) and 
the Carnegie (1909-1916), reprinted from Publication No. 175 (Vol. 3) of the Carnegie Inst, 
of Washington. 

» Phys. Rsvibw, Vol. 16. p. 183, 1903. 

* Deutsch. Phys. Gesell. Verb.. 16, p. 719, 1904. 



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422 K. MELVINA DOWNEY. 

In the present work, the primary object was to measure the natural 
ionization in a closed vessel for pressures ranging up to 20 atmospheres, 
and to eliminate, as far as possible, the ionization resulting from radio- 
active materials in the soil by performing experiments over a body of 
water of sufficient thickness to cut off such radiation. The effects of 
pressure would then give information as to the nature of the agency re- 
sponsible for the ionization. If the radiation is of an easily absorbable 
nature, the ionization will reach a saturation value at a comparatively 
low pressure; while for a range of pressures extending to even higher 
values the ionization would continue to increase in the case of the pene- 
trating radiation. That is, the more penetrating the radiation, the 
higher the pressure for which a saturation value will be obtained. A 
more detailed discussion of the ionization-pressure relations, in so far 
as they are influenced by the properties of the radiation producing the 
ionization, will be given later. Several investigators have examined the 
variation of residual ionization for pressures below one atmosphere,* 
while Wilson,* and McLennan and Burton* have made measurements for 
pressures above one atmosphere. These results will be discussed in 
connection with the distinctive features of the writer's experiments. It 
may be noted here that the pressure giving a saturation value of the 
ionization in any experiment depends upon the linear dimension of the 
ionization chamber, so that as much information may be given at a low 
pressure by a vessel of large dimensions as is given ^t a high pressure by 
a vessel of correspondingly smaller dimensions. In the course of the 
work it was desirable to observe also the variation of ionization with 
pressure when the ionization was caused by the rays from a sealed tube 
of radium bromide. These experiments, which were carried out up to 
40 atmospheres, will be described in connection with the main experi- 
ments. 

Description of Apparatus and Method. 

The form of apparatus used was suggested by Professor W. F. G. 
Swann. The general arrangement of the apparatus will be apparent 
from the diagram (Fig. i). 

The ionization chambers A and B are two cast steel spheres each 
having an internal diameter of one foot and walls one inch in thickness. 
The central rod electrode of each sphere is joined to a common wire 
which in turn is connected to the fiber of a string electroscope of the 

> For example: J. Patterson, Phil. Mag., Ser. 6. Vol. 6. p. 231, 1903, abo Kingdom. Phil. 
Mag., Vol. 33. p. 396, 1916. 

« W. Wilson, Phil. Mag., Ser. 6, Vol. 17. p. 216, 1909. 
* Phys. Rbvibw, Vol. 16, p. 184, 1903. 



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Vol. XVLI 
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VARIATION OF RESIDUAL IONIZATION, 



423 



Lutz-Edelmann type.^ The spheres are connected to the opposite ends 
of a ten megohm resistance. The mid-point of this resistance is con- 
nected to the earth terminal as are also the guard rings GG, the shielding 
tube C and the electroscope case. Connections are made at the end 
terminals of the ten megohm resistance to the source of high potential 



^.|.I. — 1.|.| 



10 MEGOHMS 



TK>em rn 





Fig. 1. 

(700 volts for the residual ionization. 

1500 volts for the ionization due to rays from small sample of Ra Br.) 
The use of the two vessels in combination with the ten megohm re- 
sistance possesses the advantage of compensating for any effects due 
to fluctuations of the batteries. These effects might otherwise, be serious 
on account of the high potentials necessary for saturation. On the other 
hand, by the use of two spheres with the ten megohm resistance, the mid- 
point of which is earthed, any alteration of the potential of the battery 
results in equal and opposite alterations of the potentials of the two 
ends of the resistance. Then the potentials of the two spheres are 
altered by equal and opposite amounts and the inductive actions of the 
two spheres on the central insulated system annul each other. The 
effect is the same as if the battery were constant. It is also apparent 

* Lutz» Physikalische Zeitschrift, Vol. 13, p. 954, 191 2. 



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424 K. MELVINA DOWNEY. [i 

that there will be compensation as regards the residual ionization at 
atmospheric pressure if this is the same for the two spheres; consequently 
the rate of deflection of the electroscope fiber is determined by the excess 
ionization resulting from the increase of pressure in the sphere A above 
the atmospheric pressure maintained in sphere B, 

It will be recalled that the string electroscope of the Lutz-Edelmann 
type consists of two parallel plates (indicated by EE in the diagram) 
with a conducting fiber stretched between them. The plates are to be 
maintained at potentials which are equal but of opposite signs. Since 
it is necessary that these potentials remain in a constant ratio, a plan 
similar to that given for the spheres was used. The plates, EE, are 
connected by a megohm, the mid-point of which is earthed and the ends 
of which are connected to the terminals of a lOO-volt battery. A prac- 
tically constant sensitivity of 10 divisions per volt was maintained 
throughout the work. For convenience a calibrating device consisting 
of a cell, potentiometer and voltmeter, V, was employed as a permanent 
part of the apparatus. It will be seen from the diagram that the central 
system was earthed through the voltmeter when the key, F, was open 
and the key, D, was closed. 

It was obviously necessary that the potential between the spheres and 
the insulated, central system be sufficiently high to secure ** saturation." 
Tests were always made to insure that there was no additional rate of 
movement of the fiber due to an increase of the potential beyond that 
assumed sufficient for saturation in any particular case. 

A mixture of resin and beeswax was employed to make the vessel A 
airtight at high pressures. The bolts were tightened while the spheres 
were sufficiently hot to retain the mixture in a liquid form; and by this 
means it was possible to make the vessel stand a pressure of 65 atmos- 
pheres without appreciable leakage. 

The pressure in A was raised by connecting a valve at its end to a 
cylinder which had been filled with compressed air from a liquid air 
machine, and the pressure was recorded by a "Bourdon" gauge. The 
air was thoroughly dried by phosphorous pentoxide placed inside the 
sphere. 

For the portion of the observations where a radio-active substance 
was required, a sample of radium bromide of the order of two milligrams 
was used. This was enclosed in a lead case, the walls of which were ij 
cm. in thickness. The lead case containing the Ra Br. was placed at a 
distance of eight feet from the spheres during the observations in which 
it was used. 

Method of Calculation. — The excess rate of production of ions per c.c. 



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No!"s^^^'] VARIATION OP RESIDUAL IONIZATION. 425 

as a result of the increase in pressure in A above atmospheric pressure is 

determined as follows : 

Let C = capacity of system, 

AF = gain in potential of the fiber in e-s units, 

e = electronic charge = 4.8 X lO"^^ e.s. units, 

V = vol. of ionization chamber in c.c, 

q = number of pairs of ions produced per c.c, per sec. 

CAV 
We then have a = — — , 
^ vet 

where t is the number of seconds for the fiber to acquire a potenital AV. 

The order of magnitude of the emanation effects from the table, 

equipment and platform would be so small that they could be disregarded 

in the calculations. 

Measurements. 

Subsidiary Experiments, 

Laboratory Conditions, — In view of the fact that a number of the experi- 
ments had to be performed in the laboratory, and since a great many 
radio-active measurements had been made in the building, it seemed 
necessary to make a thorough survey of the various laboratories so as 
to detect any effect due to any possible radio-active contamination of the 
walls. Furthermore, it was necessary to know whether there was any 
influence due to the radium known to be in the building. There were 
2 mg. of radium in solution on the top floor and there were 3 mg. of 
shielded radium kept in the vault on the first floor. The laboratory, 
where the experiments were finally carried out, was situated in the 
basement. 

The ionization chamber for these measurements was a cylindrical 
vessel having a volume of 6.8 liters. The central rod which was insulated 
from the vessel was connected to the string electrometer, and a connec- 
tion was made to the calibrating device in a manner similar to that 
already given for the main apparatus. The potential (100 volts) which 
was applied to the vessel caused the ions of the same sign to go to the 
central electrode; when the connection to earth was released, the fiber 
would deflect. The time of the deflection of the fiber for a fixed number 
of divisions was recorded. The sensitivity of the electrometer was 
maintained at 10 divisions per volt. 

The following are representative of the observations: 
Electrical Laboratory (top floor), Dec. 26, 1918, values for g: 10.4, 

8.75» 9-8, 9-0, 97» lo.o (Mean 9.6). 
Room I (Basement), Dec. 27, values for q: 9.8, 9.4, 9.2, 8.2, 8.7, lo.o 

(Mean 9.2). 



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426 K, MELVINA DOWNEY. [^j 

Room I (Basement), Jan. ii, q: 10.8, 11.7, 12.6, 12.6 (Mean 11.9). 

Room II (Basement), Jan. 11, q: 10, 12.7, 10.8, 11.7 (Mean 11.3). 

In view of the fact that the effects due to passing clouds and to the 

other conditions determining q are such variable quantities at different 

times, it is evident that there is no systematic difference between the 

values obtained for q in Room I. and Room II. To make a still more 

conclusive test, the radium in the vault was removed to the vault in the 

library building. The values obtained were these: 

Jan. 23 — Before the removal of the Ra. — 12.2, 11.9, 11.9, 11.5, 11.9, 

12.6 (Mean 12.0). 
Jan. 23 — ^After the removal of the Ra. — 12.4, 12.8, 12.4, 12.3, 12.2, 

12.9 (Mean 12.5). 
Jan. 24 — Before the return of the Ra. to the Physics Building — (10:30 to 

11:30 A. M.) — 13.8, 12.7, 12.4, 13, 12.8, 12.8 (Mean 12.9). 
Jan. 24 — ^After the return of the Ra. — (12.15 to i :oo P. M.) — 13.0, 13.7, 

12.3, 12.5, 13.2, 13.8 (Mean 13.1). 
There was apparently no effect due to the presence of this radium in the 
vault. This was also verified by experiments of an entirely different 
nature which were performed by Miss Herrick (a graduate student in 
this department).^ 

Diurnal Variation. — During the course of the preceding observations, 
a decided variation in the ionization values was noticed at times. For 
quite a number of consecutive days in January, higher values were 
obtained in the evening than in the mid-part of the forenoon. Some- 
times the difference was as much as 20 per cent. 

In the interval from January 24 to February 6, several series of observa- 
tions were taken, each series extending over a period of 24 hours. When 
the atmosphere was exceedingly clear, a maximum was obtained in the 
morning (7 to 9 A.M.) and a more decided maximum from 6:30 to 8:30 
P.M. with the values rather high during the first part of the night. 
When the sky was cloudy, no very obvious diurnal variation was ob- 
tained. The curves obtained January 26, February i and February 4 
are given in Fig. 2. January 26 was an exceptionally clear day and there 
was no appreciable change of the barometer. February i was mostly 
cloudy. The obesrvations from February 3 to February 5 were begun 
just as a snow-fall, which had continued for some time, was ceasing. 
During a part of the observations on February 4 the sky was cloudy. 

It would be desirable to continue these observations over a long period 
of time to test for the existence of the diurnal variation, particularly as 
there is not a unanimous agreement among investigators as to the 

^ Master's Thesis, University of Minnesota, 1919. 



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Vol. XVLI 
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VARIATION OF RESIDUAL IONIZATION. 



427 



existence of the diurnal variation. The results obtained are in general 
agreement with the few observations recorded by those who have found 
a diurnal variation. 

Saturation Voltage, — For the penetrating radiation the highest pressure 
used was not over 22 atmospheres. Tests for the saturation voltage 



-- Xii 2^ .10/9 




,,„ -tA. 


i^)(t^^'^iA: 


Uj^^^*^^^ 


r^T- ^, 


J5** \l 










-V^^-v 


,'"^^^^K^^ 


— ^7^7^ ^^ 


8." —" 




</) 






V L^ li y*ii% A / 


^^-va.==^'^^^^ '^ !/w yv 

K AH M Rft N 



Fig. 2. 

at this pressure were made. The potential of the end-terminals of the 
ten megohm resistance, and the corresponding values of the ionization 
current are given in Table I. 



Table I. 


Table II. 


Table III. 


Pftsswre, 22 


Atmospheres 


Pressure, 20 


Atmospheres, 


Pressure, 40 Atmospheres, 


PotlHitfal. 


lonixiitioii 

in Arbitrmry 

UniU. 


Potential. 


lonlation 

in Arbitrary 

Unite. 


Potential. 


loniiation 

in Arbitrary 

Unite. 


136 volts 


8.28 


280 volts 


13.69 


300 volts 


15.87 


272 " 


8.37 


420 " 


14.90 


600 " 


20.00 


408 " 


8.35 


560 " 


14.78 


900 " 


22.22 


544 " 


8.33 


700 " 


14.74 


1200 " 


22.27 


680 " 


8.39 






1500 " 


22.34 



It will be apparent from Table I. that for a voltage of 272 or more the 
current remained constant to within i per cent. The test for saturation 
voltage for the pressure of 20 atmospheres is given in Table II., which 
was obtained with the radium-bromide specimen in its position eight 
feet from the spheres. For the same position of the radium bromide the 
saturation voltage was also tested for a pressure of 40 atmospheres. 
The values obtained are given in Table III. It is evident from Tables 
II. and III., respectively, that 700 volts is amply sufficient for saturation 



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428 K. MELVINA DOWNEY. 

at 20 atmospheres, and 1500 volts for 40 atmospheres when the Ra Br. 
specimen is in the position described. 

Main Measurements. 
General Procedure. — ^The method of making observations follows the 
same plan as that already indicated for the preliminary work. With the 
source of potential connected to the spheres as indicated in the diagram 
(Fig. i), and the fiber insulated from earth, the rate of deflection is 
proportional to the rate of production of ions. The general plan of 
making measurements will be apparent from the data given for a set of 
observations taken over the Mississippi river, May 16. 
In order to avoid error due to leakage, the fiber is charged in such a way 
as to cross the zero during the observation and the range of scale divisions 
for any reading is so chosen that there is an equal number on each side 




Fig. 3. 

of the zero. As soon as the fiber passes the scale reading, ^1, the time 
Ti is recorded. ^3 is the position of the fiber at the time Tz. AF is 
the change in the potential of the fiber in the time Ty-Ti. For the set 
of readings above, AF was always i volt. 5i, the sensitivity of the 
electrometer before the fiber was released, as well as 52, the sensitivity 
after the fiber was earthed, were recorded. P is the pressure in sphere 



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Vol. XVI.i 
No. 5. J 



VARIATION OP RESIDUAL IONIZATION. 



429 



A in excess of one atmosphere. In order to test for constancy of condi- 
tions, the positions of the fiber were recorded both when the connection 
of the fiber to the calibrating device was released and when it was restored 
again at the end of the observation. 

Curves Obtained. — ^The curve for the data of Table IV. is given in 

Table IV. 



9i. 


«i. 


71. 


n. 


Volt«. 


Si 

(Dhrisions per 

Volt). 


A. 

(Diviiions per 

Volt). 


P. 
(Atmos- 
pheres). 


Time (Mid. 

Pt.o« 

Reading. 








Min. Sec. 












—4 


+4 





5 40.0 




8 


8 


19.35 


2:10 P.M. 


—4 


+4 





6 47.6 




8 


8 


15.35 


3:00 P.M. 


—4 


+4 





9 24.3 




8 


8 


10.2 


3:50 P.M. 


—4 


+4 





14 43.0 




8 


8 


5.12 


4:45 P.M. 


—4 


+4 





35 33.0 




8 


8 


0. 


5:40 P.M. 



Fig. 3. The reciprocals of the times (expressed in seconds) for the fiber 
to gain a potential of i volt are plotted against the pressure in A in 
excess of one atmosphere. A linear relation was obtained. To find g, 



12 


«M-* 
























/ 


14 










/ 


/ 










/? 


/ 




P It 






* 


/ 






^^ 




> 


/I 








^ ■ 




/ 










1 


/ 












{ 


r 













P£fSS(/£f \H ffmOSPHtfitS 



Fig. 4. 



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430 



K. MELVINA DOWNEY. 



the actual numbers of pairs of ions produced per c.c. per second, these 
ordinates are to be multiplied by c{i/so6)/ve 

{c = capacity of the system, 

AF = I volt = 1/300 e. s. unit, 

V = volume of sphere A in c.c. 

e = electronic charge in e. s. units). 

The observations for the full line curve given in Fig. 4 were obtained 
over the river May 17 from 10-40 A.M. to 545 P.M. 

The location of the apparatus over the water will be apparent from 
the photograph (Fig. 5). The water underneath the pier was 8i feet 




4 • ft It 



Fig. 6. 



in depth. It might also be mentioned here that for the final measure- 
ments the electrometer was suspended from a rigid frame by means of 
springs so as to ensure freedom from the effect of any mechanical dis- 
turbances near the pier. 

The curve in Fig. 6, which was obtained during the first week of May, 
is representative of other measurements taken in the laboratory. The 



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Physical Review, Vol. XVI., Second Series. Plate I. 

November, 1920. To face page 430. 



Fig. S. 



K. MELVINA DOWNEY. 



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Vol. XVLI 
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VARIATION OP RESIDUAL IONIZATION, 



431 



measurements for Fig. 7 were made in the laboratory when radium was 
placed 8 feet from the spheres as previously indicated. The brdinates 
for Fig. 4, Fig. 6 and Fig. 7 are the same as have been given for Fig. 3. 

















M 


xn-* 






















/ 




r 
1 








^ 


/^ 








/ 








1 




/ 










1 


/ 


f 










< 

• 


/ 














\ 




1 1 

rnospttt 


Res 


i 



Fig. 7. 



Discussion. 

Ionization Pressure Relations. — If the residual ionization is due for 
the most part to radio-active impurities in the walls of the vessel, the 
radiation may be of the a, j8, or j8 and 7 type, or it may be composed of 
all three types. The main part of this ionization would be due to the 
a and j8 rays. The a rays which are the more efficient ionizers would be 
absorbed by about five cm. of air at atmospheric pressure. While the /5 
rays and the secondary corpuscular rays due to them* are more pene- 
trating, practically all the soft j8 rays and some of the hard rays, which 
have a range of several meters in air, would be absorbed at higher pres- 
sures. Thus, to the extent that the ionization is due to absorbable 
radiation of this kind, the ionization per gram of gas should decrease 
with increase of pressure. If one admits the existence of a penetrating 
radiation partaking of the 7 ray nature, the ionization in the closed vessel 
may be attributed to several sources : 



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432 K. MELVINA DOWNEY. \^SSS 

(i) The direct action of the penetrating radiation in the gas; 

(2) The secondary radiation emitted from the gas by the primary 

penetrating radiation; 

(3) The secondary radiation emitted from the walls of the vessel by the 

penetrating radiation. 

In addition to these agencies it is of course possible that a portion of 
the ionization may be due to radio-active impurities. The portion of the 
ionization under (i) should be proportional to the pressure. Since 
the number of ions produced by the source (2) varies with the number of 
molecules of the gas, and with the number of electrons responsible for 
the ionization, it is apparent that this portion of the ionization would 
vary proportionally with the square of the pressure. This holds only 
to the extent that the ionization per cm. of path of the electrons is the 
same at all parts of the path, and to the extent that the penetration of 
the electrons enables them to reach the walls before coming to rest. 
When the pressure is so high that the electrons complete their paths 
within the vessel, the increase of ionization would be less rapid than the 
square law would demand. But an influence in the opposite direction is 
to be found in the increase of ionization per cm. of path toward the end 
of the range of the electrons. The latter effect would be apparent at 
pressures below that at which the former would appear. Consequently 
in regard to (2) it is possible that the curve of ionization against pres- 
sure might first show a variation according to the square of the pressure, 
then a more rapid increase than the square law would indicate, and 
finally a falling down to a linear relation when the pressure became so 
high that the penetration of all these ionizing electrons falls within the 
vessel. 

The portion of ionization due to (3) should obey a linear law until the 
pressures become so high that the more active parts of the electrons* 
paths fall within the vessel. At such pressures the ionization would 
show a more rapid increase with pressure. Finally a saturation value 
should be reached when the whole path is completed within the vessel. 

Discussion of Experimental Results. 
A survey of Fig. 3 and Fig. 4 shows that the variation in the natural 
ionization with pressure obeys a linear law up to 21.5 atmospheres. In 
view of the preceding discussion, the linear relations given in Figs. 3, 4 
and 5 indicate that the ionization within a closed vessel is not due to 
a soft radiation, but is determined either directly by a penetrating radia- 
tion of the 7 type or by a hard corpuscular radiation emitted from the 
walls of the vessel by the penetrating radiation. If it is attributed to 



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Nas?^^^*] VARIATION OF RESIDUAL IONIZATION, 433 

the corpuscular radiation, this radiation itself is then so penetrating 
that it is not appreciably absorbed in passing through a i-foot thickness 
of air at 20 atmospheres pressure. (One foot of air at 20 atmospheres 
pressure is equivalent in absorbing power to 20 feet of air at one 
atmosphere.) 

It is further apparent that for the range of pressures employed, the 
contribution to the ionization by secondary rays emitted from the gas 
by the penetrating radiation is not the primary agency at work, for, if 
it were, the curve should become convex to the horizontal axis. 

That moisture may produce an appreciable effect is shown by the 
curve of Fig. 6 which has a slight irregularity in the neighborhood of 17 
atmospheres. This curve was obtained without any additional drying 
agent other than that in connection with the compressor of the liquid 
air machine. For the curves given in Figs. 3, 4 and 7 the drying agent 
was used as mentioned. For these no such irregularity was noticed. 
It is probable that there was some water vapor present in the case of (6). 
If the water vapor in the air from the compressor were as much as one 
seventeenth saturated, water would begin to condense at about 17 
atmospheres and this would result in a change of conditions at this 
pressure. (Note: The sphere A was filled with air at the highest pressure 
used and the air was allowed to escape very slowly to reduce to the lower 
pressures.) If one considers the actual numbers of ions given by Fig. 3 
and Fig. 4 and compares them with the corresponding quantities for 
Fig. 6, it will be observed that there is little difference — those in the 
laboratory were slightly lower. Since the %\ ft. of water was amply 
sufficient to cut out practically all the radiation from the soil below in the 
case of the measurements over the river, it seems evident that the concrete 
base of the building served the same function as the water. This was 
likewise indicated by the experiments of Miss Herrick, previously men- 
tioned in this paper. For the work inside there was also the absorbing 
effect of the roof and the upper floors of the building. 

It will be noted that the curves given in Figs. 3, 4 and 6 show a notice- 
able ionization for zero pressure. This is no doubt due to a soft radiation 
from the walls of the sphere A , in which the pressure was varied. Before 
the compressed air was admitted into sphere A, it was left in a cylinder 
for a time so as to allow any radium emanation present to decay partially. 
However since the cylinder containing the air was not allowed to stand 
the same length of time before each set of observations, there would be 
different amounts of emanation admitted into the sphere. For the 
observations at the higher pressures, it was found necessary to wait a 
time after the pressure was lowered for a constant rate of deflection of 



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434 ^- MELVINA DOWNEY. [ISSS! 

the electrometer. This was due to the fact that it required time for the 
old decay products to come into equilibrium with the new amount of 
radium emanation. (A part of the emanation would be removed with 
the air while the pressure was being lowered.) It may be mentioned 
here that the radium emanation in air at ordinary atmospheric pressure 
is not responsible for more than 1.7 ions per c.c. per second. 

For the purpose of comparison it was naturally of interest to test the 
ionization produced due to the effect of 7 rays of radium when the pres- 
sure within the sphere A was varied. What has been given in the 
discussion of the ionization pressure relations under (i), (2) and (3) 
may be considered as applying here — the penetrating radiation for the 
case being the 7 rays of radium and the secondary radiation from the 
walls and gas being rays of the j8 and 7 type. 

The curve of Fig. 7 indicates an increase of ionization with pressure. 
The ionization per gm. of air at pressures below 4 atmospheres is ob- 
viously somewhat larger on account of the soft radiation which is then 
effective. In curve 7 which has an approximately linear relation for the 
range of pressures from 4 to 20 atmospheres, it is noticed that the slope 
changes at about 20 atmospheres to a value approximately 0.6 of that 
for the pressures below 20 atmospheres. This departure from linearity 
is doubtless due to those j8 rays which complete their paths within the 
spheres at this pressure. Twenty atmospheres would be sufficient to 
absorb j8 rays having a penetration as great as 6 meters in air in one 
atmosphere. Those having a longer range would still be unabsorbed 
as would also those j3 rays having their paths along the shorter chords 
of the sphere. The results at the highest pressure indicate a tendency 
toward a more rapid increase of the ionization with pressure. This 
suggests an effect due to the secondary radiation from the air. However, 
it is not possible to attach much importance to this until observations 
have been made for still higher pressures. 

It is desirable to compare the results given in this investigation with 
those found by other observers. Patterson, who measured the natural 
ionization in a closed vessel for pressures extending only to 80 cm of 
mercury, obtained results which indicate a marked departure from 
linearity over this range. From this Patterson draws the conclusion 
that the natural ionization is due to radio-active impurity in the vessel. 
The actual ionization for one atmosphere was as much as 40 ions per c.c. 
per second, so that without question there was an unusually large 
amount of radio-active impurity in the walls of the vessel used by Patter- 
son. A large number of the ions he obtained was probably due to the 
a particles so that he naturally found the effect per gram to diminish 



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Was ] VARIATION OF RESIDUAL IONIZATION. 435 

with increase of pressure (on account of the short range of the a particles). 
In reality the true residual ionization can have formed only a small part 
of the total effect measured in his experiment. In the writer's experiment 
results were never considered reliable unless the vessel had been so 
thoroughly cleaned that the ionization ranged from 10 to 13 or 14 ions 
per c.c. per second. 

Additional results on natural ionization which were obtained by 
McLennan and Burton indicate an increase of ionization for the range 
of pressures used (4.4 to 500 cm.), but the graph was not linear. The 
slope of the tangent of curve at one atmosphere is about twice that at 
seven atmospheres. Unfortunately McLennan and Burton have not 
stated any actual values for **g." It is therefore impossible to form any 
opinion as to whether the departure from linearity may have been due 
to radio-active impurities in the walls of the vessel. However, they do 
give some evidence of the existence of the radio-active impurities in their 
experiments. 

If the ionization in a closed vessel is primarily due to the corpuscles 
emitted from the walls of the vessel by the external radiation, departure 
from linearity is to be expected when the pressure attains a value so 
high that the linear dimensions of the vessel become comparable with 
the electronic penetration at that pressure. Thus in comparing the 
results of the different observers it is to be noted that the departure from 
linearity is determined not by the pressure, but by the product of the 
pressure and a quantity of the order of the linear dimensions of the vessel. 
In other words, experiments in a chamber of average dimensions, 30 cm., 
give at 20 atmospheres as much information in regard to this phase as 
experiments made up to 60 atmospheres in a vessel of only 10 cm. 
linear dimensions. 

The results of W. Wilson are of interest in that they indicate an increase 
of the natural ionization with pressure. While he used pressures as 
high as 45 atmospheres, the results he obtained can be compared with 
those of the writer only at those pressures below 15 atmospheres since his 
ionization chamber had less than | the dimensions of that used in the 
present investigation. The electroscope which recorded the measure- 
ments consisted of a vessel 10 cm. cube. This was also used as the 
ionization chambers. The small sensitivity and large leakage in Wilson's 
experiments made it impossible for him to obtain results with a high 
degree of accuracy. The electroscope leaf was maintained at a potential 
of 200 volts. Since in the writer's experiments the change in potential 
of the fiber by the natural ionization was not over i volt in the time 
necessary for a reading, it is evident that Wilson's leaf system could not 



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436 K. MELVINA DOWNEY. ^^SS, 

have registered this with any high degree of accuracy. The writer has 
plotted in Fig. 4 the values of Wilson for pressures above one atmosphere 
(these are indicated by means of crosses on the dotted curve). The slope 
of the linear part of Wilson's curve has been made the same as that of the 
line obtained by the writer. It will be noted that the departure from 
linearity of the author's results is never more than 1.30 per cent, of the 
highest value measured while the corresponding quantity for Wilson's 
results is as high as 10.50 per cent. 

Wilson also obtained an ionization pressure curve for the case where 
radium-bromide was placed outside the ionization chamber and the pres- 
sures were varied up to 40 atmospheres. From what has been said it is 
clear that this would amount to a range of approximately 13 atmospheres 
in the writer's experiments. Wilson obtains a maximum at this pressure 
probably for the reason tl^at he did not have saturation voltage. At 
atmospheric pressure he works with a value for q amounting to 216 
ions per c.c. per second which is almost four times that obtained in the 
present experiment at atmospheric pressure. It was possible for the 
writer to work with a weak radio-active specimen on account of the com- 
pensating arrangement (the 2 spheres in combination with the ten 
megohm resistance). Furthermore the radium-bromide was shielded to 
such an extent that the 7 rays reaching the ionizaiton chamber and con- 
sequently the secondary corpuscular radiation due to the 7 rays were 
much harder than the radiation which was responsible for the ionization 
in Wilson's experiments. This would naturally cause Wilson's curve to 
depart from linearity sooner than the writer's curve. 

Additional measurements on the ionization in a closed vessel due to 
the effect of the 7 rays of radium have been made by Kaye and Laby* 
as well as D. C. H. Florance,* but it will be seen that the range of pres- 
sures is rather limited when compared with the conditions of the present 
investigation. These observers worked with ionization vessels the plates 
of which were not over 2 cm. apart. In the work of Kaye and Laby 
there was a central electrode about i cm. from the sides of the vessel, 
so that as regards ionization by electrons emitted from the walls of the 
vessel their curve, which was obtained for a range of pressures up to 17 
atmospheres, could be compared with that of the writer only for pressurse 
below one atmosphere. 

D. C. H. Florance who used pressures up to 80 atmospheres worked 
with the plates i cm. apart, with an additional reading for a distance of 
2 cm. between the plates. For the spheres used in the present experi- 

» Kaye and Laby, Phil. Mag., Ser. 6, Vol. 16, p. 879, 1908. 
«D. C. H. Florance. Phil. Mag., Ser. 6, Vol. 25, p. 172, 1913. 



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No'^s^^^*] VARIATION OF RESIDUAL IONIZATION. 437 

ment, the former condition would correspond to a pressure of 5 atmos- 
pheres and the latter to a pressure of 10 atmospheres. The inability of 
Florance to secure saturation voltage at the higher pressures is no doubt 
due to the unusually large amount (30 mg.) of radium-bromide used. 
Without saturation a large change in slope would be expected at the 
higher pressures. 

In conclusion it is a pleasure to acknowledge my gratitude to Professor 
W. F. G. Swann, who has suggested the problem and directed the investi- 
gation. To him I extend my best thanks for the encouragement and 
advice has has given throughout this work. 

I wish to thank Professor H. A. Erikson for his continued interest 

in the work, and also Mr. C. H. Dane, mechanician, for assistance in 

the solution of mechanical difficulties. 

Dbpartmsnt op Physics. 

University op Minnesota, 
December, 1919. 



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438 WARREN WEAVER. 



THE KINETIC THEORY OF MAGNETISM. 

By Warren Weaver. 

Synopsis. 
Magnetic Susceptibility of Gases. — The results of a previous paper by Honda and 
Okuba (Phys. Rev., Vol. 13, 1919, p. 6) are considered, certain important errors 
noted, and some aspects of the assumptions further examined and developed. 
The susceptibility is not the same whether or not the gyroscopic nutation of the 
molecules persists, and the apparent check with Langevin's result is shown to be in 
error. A gas is shown to be diamagnetic or paramagnetic, on this theory, according 
as the nutation does or does not persist. This lesult holds, at least without further 
investigation, only for smooth spherical molecules rather than as stated. A discus- 
sion is given of the efifect of thermal impacts on gyroscopic motion of this type. 

I. In a recent paper^ Professors Honda and Okubo have worked out 
in considerable detail a kinetic theory of magnetism, which takes account 
of the gyroscopic precessions and nutations which the molecules of a 
gas will execute under the torque of an applied magnetic field. Some of 
their results will here be subjected to a critical examination. It will 
be necessary to duplicate some of their preliminary work so that matters 
of notation will be clear. 

A given molecule is considered to be initially a magnet of moment Jlf, 
which implies that the distribution of electronic orbits within it is such 
that the magnetic field produced by the separate electrons is such that 
they do not completely neutralize each other at exterior points. The 
change — 6M in this moment caused by the growth of the external field 
from a value zero to a final value H is not considered, it being supposedly 
very small as compared to the other effects considered. The magnetic 
axis of this molecule makes an initial angle a with the direction of the 
applied field. Suppose that this molecule is rotating about some axis, 
not in general coinciding with its magnetic axis. It will then have a 
component of magnetic moment along the direction of the axis of rota- 
tion, and one normal to this direction. Consider first the effect of the 
former component, assuming that the actions caused by the two com- 
ponents take place independently. The molecule will start to fall 
towards the direction of the field, the precession beginning as soon as 
the incipient fall develops, and the axis will perform ordinary precession 
about the direction of the field, and nutation about the steady precession. 

* Phys. Rbv., Vol. 13, 1919. p. 6. 



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Na*5?^^] ^^^ KINETIC THEORY OF MAGNETISM. 439 

What will then be the magnetic moment of the gas which is induced by 
the field Wi The original orientation of magnetic axes was isotropic, 
else the gas would have been originally magnetic, so that the number 
of axes which originally made with the direction of H an angle lying 
between a and a + da would be 

dn = \ sin ada. (i) 

The motion of the axis is such that, as the nutation takes place, the 
angle between the direction of the axis and H lies between the original 
value a, as an upper limit, and an angle ^1, as a lower limit, where Bi is 
given by the equation 

^ . / . 2 cos a I . . 

where 

a__ MH 

K being the moment of inertia of the molecule about its axis of rotation, 

and 0) the angular velocity of spin about this axis. For small values 

of a this gives 

a fl* 

cos ^1 = cos a + - (i — cos' oc) -\ — (cos* a — cos a) 

2 2 



A — I 3 cos' a cos* a ) + 

4 V^ 2 2/^ 



(4) 



II. The first important point to be noted now appears. The definition 
of a given by equation (3) differs from that given in the previous paper 
by a factor 2. The equation was given as 

MH . . 

a=-^^-,, (3a) 

a value which, when substituted in (2) above does not give a correct 
result. Comparing (3) above with Langevin's definition of his quantity 
a we find that they are not the same. For clearness let us write Lange- 

vin's result 

I = JlfH(coth.4 - iM). (5) 

in which 

A = ^ij^ , (6) 

in which r is the gas constant referred to a single molecule. Langevin 
was considering, in the original paper in which this result appeared,* 
a gas such as oxygen the molecules of which have, as is indicated by the 

» Ann. de Chim. et de Phys., V., p. 70, ipoS- 



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440 WARREN WEAVER. [^SS! 

ratio of the specific heats, two degrees of freedom in rotation. Cor- 
responding to each of these degrees of freedom will be an amount of 
energy ^rT, or, for the total energy of rotation, rT. Since in the above 
work the reference axes in the molecule were so chosen that the expression 
JXw* is the whole energy of rotation it is equal to rT. Thus we have 

2i4 = a. (7) 

Thus the values of a and A are not the same, as was stated. 

Concerning this'point Professor Honda has written me, in answer to a 
letter sent him before the present paper was written, the following 
statement. '* Our value of ' a ' does not differ from that of Langevin. 
Your calculation is also quite correct. Our writing in p. 147 (Sci. Rep.)^ 
is incorrect, but its content is correct. In considering a magnetic 
molecule rotating about its axis as a gyroscope acted upon by the force 
of gravity (g = H) we must take OA as the distance between the fixed 
point and the center of gravity of the equivalent gyroscope, but not AB. 
Hence in passing from the problem of the gyroscope to the molecular 
magnet half the pole distance must be taken in consideration. Hence 



^+mJf 




Fig. 1. 

in the first equations of gyroscopic motion we must put ilf /2 for M, 
And consequently 

^MH ^ ^\2)^ MH 

a = -^^ becomes -^J^^^k^^^ 

which is Langevin 's 'a.'" 

Insofar as I understand this statement I believe it to be incorrect. 
The first equation of motion of the gyroscope in which the quantity M 
appears is an equation which expresses the fact that the sum of the 
kinetic and potential energies of the gyro-molecule remains constant. 
The potential energy of a magnetic doublet of this sort of magnetic 
moment M {= mr) when making an angle $ with a field H is surely 

» The text of the article in the Science Reports of the Tohoku Imperial University here 
teferred to is the same as that which appeared in the Physical Rbvibw. 



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JJSr^] THE KINETIC THEORY OP MAGNETISM. 44 1 

— MH COS B, The above statement seems to oflfer no satisfactory 
justification for replacing M in this expression by Af/2. 

III. In the previous article two cases are considered separately; i.e., 
that in which the nutation persists, and that in which it does not. A 
discussion of which of these two descriptions is more likely to fit the 
actual case is curtailed because the result is there obtained that for small 
values of a the magnetic moment is the same in the two events. It 
seems clear on simple and general grounds that this can not be the case. 
If the precession were to take place at the larger limit of the angle which 
measures the nutation, — that is at a itself the magnetic moment would 
obviously be zero, the isotropic character of the orientations not having 
been changed. If the nutation is damped out in some way, or if, as 
suggested, the field is applied infinitely slowly so that the precession 
takes place steadily at the lower limit ^1, the magnetic moment is com- 
puted to be given by the equation 

<^/<^o = a/3. (8) 

Now if the nutation actually takes place the direction of the rotation 
axis varies between an angle a and an angle Bi with the direction of the 
field, so that one would expect the time mean of the magnetic moment 
to lie between the two values which correspond to the two extreme 
positions, namely, between zero and fl/3. One turns then to the analysis 
to see where such an error could have arisen. It is found, apparently, 
in the equation near the bottom of page 13, which should read: 

fdB\^ 
k sin* ^ I "7. 1 = 2 JIf H(cos B — cos a)(cos B — cos ^1) ( — cos B% — cos B) , (9) 

in which there has been inserted a factor 2 on the right-hand side, and a 
necessary minus sign in the last term. If the calculation is carried out 
from this point the result obtained is 

<r/<ro = a/6 -f 0.24a* + • • • (10) 

or, for small values of a, 

<r/<ro = a/6. (ii) 

This result could have been anticipated, and, indeed, obtained by 
means of a much simpler calculation. The angular velocities of spin 
with which we have to deal are large^ of the order of 10" radians/sec. 
while the applied couples are small, corresponding to small values of a. 
The precession is therefore very slow, and the nutation very rapid, 
being moreover between very small limits. For this case the motion 
may be described as a steady precession combined with a nutation in 

1 Tak4 Son^, Phil. Mag.. March. 1920, p. 348. 



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442 WARREN WEAVER, [^^^ 

an ellipse about the point which advances with the regular precession^. 
This steady precession takes place at an angle of inclination to the direc- 
tion of the field which lies half-way between a and ^i.* Since this ellipti- 
cal motion is harmonic the time mean will be the same as if the axis 
precessed steadily at an angle equal to the mean of a and ^i. 

This gives us at once for the magnetic moment per gram molecule of 
the gas 



= I cos I I sm ada (12) 



or 



<r I rf Bi a . $1 . a\ , ^ . . 

— = - I I cos— COS sm — sm — I sm ada. (13) 

<^0 2 Jq \ 2 2 2 2/ 

Making use of (4) we find 

$1 a d a a 

cos — = cos — h - cos— sin* , (14) 

2 2222 ^ ^^ 



. $1 , a a , c 
sm — = sm sm — cos' 



^2- . 



Which in (13) give 

<r I f / a . \ . 

— = - I I cos a + -sin* a 1 sin ada, (15) 

(Tq 2Jo \ 4 / 



(16) 



(T a 

(To 6 * 

If (5) is expanded in a power series in A the result is obtained 

(TO 3 90 ^ '^ 

It is thus found that the results obtained when the nutation does and 
does not persist are different, as given by equations (16) and (8) respec- 
tively, and that in only one case does the result check that of Langevin, 
which, written in terms of a, is 

<r a a^ ^ , ^. 

— =----r-+ •••. (18) 

(To 6 360 ^ ' 

The result of Langevin is thus seen to be the same, for small values of a 
as that obtained from a study of the gyroscopic motion, provided only 
that the nutation persists. It should be pointed out, however, that 
this check probably has no significance, and there is no reason why one 
should expect a check; for Langevin's result is a complete result, while 

* A. G. Webster, Dynamics of a Particle, etc., page 286. 

* Andrew Gray, Gyrostatics and Rotational Motion, page loi. 



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No"^^^ J ^^^ KINETIC THEORY OF MAGNETISM, 443 

the result given by (16) is a partial result obtained from a study of one 
component only of the magnetic moment. The check would be actual, 
rather than merely apparent, only if the magnetic axes of all the mole- 
cules happened to coincide with their spin axes. With the ordinary 
picture of a molecule this is exactly what one would expect would not 
be the case. For example the magnetic axis of a hydrogen molecule 
will be along the line joining the nuclei, while the rotation as caused by 
thermal impact could probably have no component in this direction. 

IV. If now the assumption is made that the axes of rotation of the 
molecules are isotropically oriented with respect to the magnetic axes,, 
so that the number whose magnetic axis makes an angle lying betweea 
ip and ip -\- dip with the axis of rotation is given by an expression similar 
to (i) we can compute that part of the magnetic moment per gram 
molecule of the gas which is due to the component of magnetic moment 
in the direction of the axes of rotation. For if we now let M represent 
the total magnetic moment of a molecule the component of M along 
the spin axis will be M cos ^, where dn ^ \ sin tpdtp molecules have their, 
magnetic axes making an angle with their axes of rotation lying betweem 
ip and ip + dip. These dn molecules contribute, according to (16), dn 
magnetic moment^ 

a' Mna f 

da = M cos ipdn X 7" = I cos* ip sin tpdip^ 

6 12 Jo 

Mna 

^ = 78"' (^9) 

<T a 

7rTr (20) 

Combining this result with that obtained in the previous paper for that 
part of the magnetic moment per gram molecule which is due to the 
component of magnetic moment perpendicular to the axis of rotation 
we have for the complete result 

(T a a a 

It is thus seen that the magnetic susceptibility is diamagnetic if the 
nutation persists. If the nutation does not persist the calculation given 
in the previous article holds, and the result is a paramagnetic suscepti- 
bility of the same numerical magnitude. 

This result will be restated, laying special emphasis upon the hypo- 
theses under which it has been obtained. There are three chief assump- 

* The notation of the previous article is used in the following equations. 



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444 WARREN WEAVER. [^SSS^ 

tions involved: that the magnetic axes are isotropically oriented with 
respect to the spin axes, that the gyroscopic motion discussed takes 
place sensibly independently of and undisturbed by whatever hastening 
and retarding of the spin is caused by the component of magnetic moment 
normal to the spin axis, and that (at least on the average) thermal impacts 
do not disturb the complexion of the system. Under these conditions 
a gas is paramagnetic or diamagnetic according as the nutation of the 
gyroscopic motion is damped out or persists. In general it would seem 
theoretically possible to determine experimentally whether or not it 
persists by investigating whether there is a rise in temperature, otherwise 
unexplainable, when the gas is placed in a field: for if this motion is 
damped out the energy thus subtracted would have to be redistributed 
between the different degrees of freedom of the gas, and therefore would 
appear, in part at least, as ordinary heat motion. In the case of a gas 
satisfying the conditions above stated the matter could be settled more 
easily by simply observing whether the gas was paramagnetic or diamag- 
netic. If for any reason the nutation was partially damped out a value 
intermediate to the two above-stated results might be expected. The 
intervals of time associated with the motions of a molecule are very small 
indeed, and it is perhaps possible that ordinarily fields are brought into 
existence at a rate which could be considered infinitely slow as measured 
in such units, in which case one would perhaps expect to find the pre- 
cession taking place steadily at the lower limit ^i, and the result thus 
paramagnetic. However for those gases which come under this theory 
the facts of experiment will settle definitely this question. 

IV. The first of the three assumptions above stated is that the mag- 
netic axes are distributed by chance uniformly with re